(CNN) Hillary Clinton is itching to take on Donald Trump in a one-on-one contest for the White House -- but she isn't pushing Bernie Sanders off the stage yet.

Democrats close to Clinton and the man who could become a top surrogate -- President Barack Obama -- insist they won't pressure the Vermont senator to leave. That reluctance is based on fear inside the Democratic establishment that such a move would make it more difficult to unite the party later this year.

After conceding the presidency to Trump in a phone call earlier, Clinton addresses supporters and campaign workers in New York on Wednesday, November 9. Her defeat marked a stunning end to a campaign that appeared poised to make her the first woman elected US president.

Clinton addresses a campaign rally in Cleveland on November 6, two days before Election Day. She went on to lose Ohio -- and the election -- to her Republican opponent, Donald Trump.

Clinton addresses a campaign rally in Cleveland on November 6, two days before Election Day. She went on to lose Ohio -- and the election -- to her Republican opponent, Donald Trump.

Clinton arrives at a 9/11 commemoration ceremony in New York on September 11. Clinton, who was diagnosed with pneumonia two days before, left early after feeling ill. A video appeared to show her stumble as Secret Service agents helped her into a van.

Obama hugs Clinton after he gave a speech at the Democratic National Convention in Philadelphia. The president said Clinton was ready to be commander in chief. "For four years, I had a front-row seat to her intelligence, her judgment and her discipline," he said, referring to her stint as his secretary of state.

Obama hugs Clinton after he gave a speech at the Democratic National Convention in Philadelphia. The president said Clinton was ready to be commander in chief. "For four years, I had a front-row seat to her intelligence, her judgment and her discipline," he said, referring to her stint as his secretary of state.

After Clinton became the Democratic Party's presumptive nominee, this photo was posted to her official Twitter account. "To every little girl who dreams big: Yes, you can be anything you want -- even president," Clinton said. "Tonight is for you."

After Clinton became the Democratic Party's presumptive nominee, this photo was posted to her official Twitter account. "To every little girl who dreams big: Yes, you can be anything you want -- even president," Clinton said. "Tonight is for you."

Clinton walks on her stage with her family after winning the New York primary in April.

Clinton walks on her stage with her family after winning the New York primary in April.

Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015.

Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015.

U.S. Sen. Bernie Sanders shares a lighthearted moment with Clinton during a Democratic presidential debate in October 2015. It came after Sanders gave his take on the Clinton email scandal. "The American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails. Let's talk about the real issues facing the United States of America."

U.S. Sen. Bernie Sanders shares a lighthearted moment with Clinton during a Democratic presidential debate in October 2015. It came after Sanders gave his take on the Clinton email scandal. "The American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails. Let's talk about the real issues facing the United States of America."

Clinton testifies about the Benghazi attack during a House committee meeting in October 2015. "I would imagine I have thought more about what happened than all of you put together," she said during the 11-hour hearing. "I have lost more sleep than all of you put together. I have been wracking my brain about what more could have been done or should have been done." Months earlier, Clinton had acknowledged a "systemic breakdown" as cited by an Accountability Review Board, and she said that her department was taking additional steps to increase security at U.S. diplomatic facilities.

Clinton testifies about the Benghazi attack during a House committee meeting in October 2015. "I would imagine I have thought more about what happened than all of you put together," she said during the 11-hour hearing. "I have lost more sleep than all of you put together. I have been wracking my brain about what more could have been done or should have been done." Months earlier, Clinton had acknowledged a "systemic breakdown" as cited by an Accountability Review Board, and she said that her department was taking additional steps to increase security at U.S. diplomatic facilities.

Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015.

Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015.

Clinton ducks after a woman threw a shoe at her while she was delivering remarks at a recycling trade conference in Las Vegas in 2014.

Clinton ducks after a woman threw a shoe at her while she was delivering remarks at a recycling trade conference in Las Vegas in 2014.

Obama and Clinton bow during the transfer-of-remains ceremony marking the return of four Americans, including U.S. Ambassador Christopher Stevens, who were killed in Benghazi, Libya, in September 2012.

Obama and Clinton bow during the transfer-of-remains ceremony marking the return of four Americans, including U.S. Ambassador Christopher Stevens, who were killed in Benghazi, Libya, in September 2012.

Clinton arrives for a group photo before a forum with the Gulf Cooperation Council in March 2012. The forum was held in Riyadh, Saudi Arabia.

Clinton arrives for a group photo before a forum with the Gulf Cooperation Council in March 2012. The forum was held in Riyadh, Saudi Arabia.

Clinton checks her Blackberry inside a military plane after leaving Malta in October 2011. In 2015, The New York Times reported that Clinton exclusively used a personal email account during her time as secretary of state. The account, fed through its own server, raises security and preservation concerns. Clinton later said she used a private domain out of "convenience," but admits in retrospect "it would have been better" to use multiple emails.

Clinton checks her Blackberry inside a military plane after leaving Malta in October 2011. In 2015, The New York Times reported that Clinton exclusively used a personal email account during her time as secretary of state. The account, fed through its own server, raises security and preservation concerns. Clinton later said she used a private domain out of "convenience," but admits in retrospect "it would have been better" to use multiple emails.

In this photo provided by the White House, Obama, Clinton, Biden and other members of the national security team receive an update on the mission against Osama bin Laden in May 2011.

In this photo provided by the White House, Obama, Clinton, Biden and other members of the national security team receive an update on the mission against Osama bin Laden in May 2011.

The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010.

The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010.

Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010.

Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010.

Obama is flanked by Clinton and Vice President-elect Joe Biden at a news conference in Chicago in December 2008. He had designated Clinton to be his secretary of state.

Obama is flanked by Clinton and Vice President-elect Joe Biden at a news conference in Chicago in December 2008. He had designated Clinton to be his secretary of state.

Obama and Clinton talk on the plane on their way to a rally in Unity, New Hampshire, in June 2008. She had recently ended her presidential campaign and endorsed Obama.

Obama and Clinton talk on the plane on their way to a rally in Unity, New Hampshire, in June 2008. She had recently ended her presidential campaign and endorsed Obama.

Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007.

Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007.

Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003.

Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003.

Sen. Clinton comforts Maren Sarkarat, a woman who lost her husband in the September 11 terrorist attacks, during a ground-zero memorial in October 2001.

Sen. Clinton comforts Maren Sarkarat, a woman who lost her husband in the September 11 terrorist attacks, during a ground-zero memorial in October 2001.

Clinton makes her first appearance on the Senate Environment and Natural Resources Committee.

Clinton makes her first appearance on the Senate Environment and Natural Resources Committee.

Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year.

Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year.

President Clinton makes a statement at the White House in December 1998, thanking members of Congress who voted against his impeachment. The Senate trial ended with an acquittal in February 1999.

President Clinton makes a statement at the White House in December 1998, thanking members of Congress who voted against his impeachment. The Senate trial ended with an acquittal in February 1999.

The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998.

The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998.

Clinton looks on as her husband discusses the Monica Lewinsky scandal in the Roosevelt Room of the White House on January 26, 1998. Clinton declared, "I did not have sexual relations with that woman." In August of that year, Clinton testified before a grand jury and admitted to having "inappropriate intimate contact" with Lewinsky, but he said it did not constitute sexual relations because they had not had intercourse. He was impeached in December on charges of perjury and obstruction of justice.

Clinton looks on as her husband discusses the Monica Lewinsky scandal in the Roosevelt Room of the White House on January 26, 1998. Clinton declared, "I did not have sexual relations with that woman." In August of that year, Clinton testified before a grand jury and admitted to having "inappropriate intimate contact" with Lewinsky, but he said it did not constitute sexual relations because they had not had intercourse. He was impeached in December on charges of perjury and obstruction of justice.

The Clintons dance on a beach in the U.S. Virgin Islands in January 1998. Later that month, Bill Clinton was accused of having a sexual relationship with former White House intern Monica Lewinsky.

The Clintons dance on a beach in the U.S. Virgin Islands in January 1998. Later that month, Bill Clinton was accused of having a sexual relationship with former White House intern Monica Lewinsky.

The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997.

The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997.

The Clintons hug as Bill is sworn in for a second term as President.

The Clintons hug as Bill is sworn in for a second term as President.

Clinton waves to the media in January 1996 as she arrives for an appearance before a grand jury in Washington. The first lady was subpoenaed to testify as a witness in the investigation of the Whitewater land deal in Arkansas. The Clintons' business investment was investigated, but ultimately they were cleared of any wrongdoing.

Clinton waves to the media in January 1996 as she arrives for an appearance before a grand jury in Washington. The first lady was subpoenaed to testify as a witness in the investigation of the Whitewater land deal in Arkansas. The Clintons' business investment was investigated, but ultimately they were cleared of any wrongdoing.

Clinton accompanies her husband as he takes the oath of office in January 1993.

Clinton accompanies her husband as he takes the oath of office in January 1993.

During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus.

During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus.

In June 1992, Clinton uses a sewing machine designed to eliminate back and wrist strain. She had just given a speech at a convention of the International Ladies' Garment Workers Union.

In June 1992, Clinton uses a sewing machine designed to eliminate back and wrist strain. She had just given a speech at a convention of the International Ladies' Garment Workers Union.

Bill Clinton comforts his wife on the set of "60 Minutes" after a stage light broke loose from the ceiling and knocked her down in January 1992.

Bill Clinton comforts his wife on the set of "60 Minutes" after a stage light broke loose from the ceiling and knocked her down in January 1992.

The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President.

The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President.

Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985.

Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985.

In 1975, Rodham married Bill Clinton, whom she met at Yale Law School. He became the governor of Arkansas in 1978. In 1980, the couple had a daughter, Chelsea.

In 1975, Rodham married Bill Clinton, whom she met at Yale Law School. He became the governor of Arkansas in 1978. In 1980, the couple had a daughter, Chelsea.

Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974.

Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974.

Before marrying Bill Clinton, she was Hillary Rodham. Here she attends Wellesley College in Massachusetts. Her commencement speech at Wellesley's graduation ceremony in 1969 attracted national attention. After graduating, she attended Yale Law School.

Before marrying Bill Clinton, she was Hillary Rodham. Here she attends Wellesley College in Massachusetts. Her commencement speech at Wellesley's graduation ceremony in 1969 attracted national attention. After graduating, she attended Yale Law School.

Hillary Clinton accepts the Democratic Party's nomination for president at the Democratic National Convention in Philadelphia on July 28, 2016. The former first lady, U.S. senator and secretary of state was the first woman to lead the presidential ticket of a major political party.

Hillary Clinton accepts the Democratic Party's nomination for president at the Democratic National Convention in Philadelphia on July 28, 2016. The former first lady, U.S. senator and secretary of state was the first woman to lead the presidential ticket of a major political party.

Clinton needs the excited supporters that have rallied around Sanders and hopes treating the senator's campaign respectfully will make them more likely to back her against Trump. Clinton has already started to make overtures to Sanders' supporters -- pledging to support them even if they don't support her -- and campaign aides have said those will continue in the coming weeks.

Clinton on Wednesday told CNN's Anderson Cooper said she isn't pushing Sanders to hurry up.

"I'm not calling myself that (the presumptive nominee)," Clinton said. "I know there are some contests ahead and I respect Sen. Sanders and whatever choices he's making. And I have a lot of empathy about this, Anderson. You know, I ran to the very end in 2008."

Obama's White House agrees there's no rush.

"The key here is unifying the party," said one Democrat familiar with the White House's thinking. "So with that in mind, we are being careful to let the process play through and provide the space for there to be a unifying moment for Hillary Clinton and Bernie Sanders."

The Democratic contest may march on but the party's infrastructure is already preparing for a Clinton nomination and the former secretary of state is starting to put general election plans into place. While Sanders will continue to campaign across the country -- including planned stops in West Virginia on Thursday -- pledging to fight until the convention, Clinton's aides said this week that she will pursue a two-prong strategy for the coming weeks: Campaign in every upcoming primary while also making trips to general election battleground states.

That strategy, though, has not quelled the nerves of Democrats across the country, who are worried that without any GOP rivals, Trump will now turn his entire focus to Clinton, possibly defining her early and hurting efforts to rehabilitate her already dinged image.

After Trump all but locked up the nomination on Tuesday night , Clinton surrogates and supporters asked the campaign's top aides whether they can use their TV and online platforms to start asking for the Vermont senator to get out of the way.

The answer they got back was a resounding no.

"The campaign won't give us the green light to tee off on him," said one supporter who asked. "It was all good to say 'Bernie should stay in' when Trump was running against other people but now that she has to take on his attacks and Trump's attacks, things have changed."

The supporter added, "To Secretary Clinton's credit, she won't let anybody start pushing him out."

Obama isn't jumping in yet

The Democratic figure who could provide her campaign a unifying boost -- Obama -- remains on the sidelines of his own party's contest.

The White House on Wednesday wasn't offering any major shifts in its strategy to elect another Democrat to the Oval Office, aside from predicting that Obama's now-regular attacks on Trump would only ramp up.

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Obama has taken to dinging Trump on an almost weekly basis, even as his administration begins preparing for the intelligence and defense briefings to which all nominees are entitled.

The latest example came Monday, when Obama told WMUR that Trump wasn't "equipped to deal with the problems of this office." Aides say he enjoys those opportunities, even if he outwardly seems dismissive of the political circus.

For Obama, ensuring the Democratic Party emerges from its nominating process intact has meant saying or doing little that would appear to favor Clinton, even as it remains obvious he sees his former secretary of state as a more predictable caretaker of his legacy.

The coalition that helped bring Obama into office has largely split between the two Democratic candidates: young people for Sanders, minorities for Clinton, and college-educated whites divided between the two. Even Obama has acknowledged that convincing those groups to vote could pose a challenge.

Democratic officials say Obama will likely target those audiences when he eventually does hit the campaign trail later this year. Without revealing any firm plans, they say stops on college campuses are likely, as are visits to swing states where his presence could boost turnout, like North Carolina and Nevada.

"There is no denying the President will have an active role in the general election," White House press secretary Josh Earnest told reporters aboard Air Force One Wednesday. "There are six months until Election Day. I'm confident the President will spend many of those days between now and Election Day making a strong case about the progress our country has made over the last eight years."

Campaign trail

Vice President Joe Biden, meanwhile, will reprise the role he's played in past contests, campaigning in places where his connection to working-class voters could provide a lift to a Democratic candidate. One official identified Pennsylvania, Ohio, and Michigan as likely stops for the Vice President in the general election.

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Both Obama and Biden have endorsed Democratic Senate candidates, and will likely continue eyeing down-ballot races. The President also remains a draw for deep-pocketed Democratic donors, and his fundraising schedule will continue apace in the coming months.

With entire chapters of his presidential legacy riding on who succeeds him, no one has more stake in the party coming together than Obama. And as the Democrat that both Clinton and Sanders supporters can love, he stands the best shot at keeping the warring factions from inflicting mortal wounds.

To that end, Democratic officials aligned with Obama say they're closely watching Sanders' tone as the race moves toward its final stages. But there's zero effort to push the Vermont senator from the race -- either explicitly or behind the scenes.

The Clinton campaign has so far been effective at stopping high level surrogates and supporters from telling Sanders to get out of the way, and the White House has helped in the effort.

Proof of that success: Even Priorities USA, the pro-Clinton super PAC that will spend millions to hit Trump and defend Clinton in the general, said Wednesday that they will not call on Sanders to get out.

"Since the results in Arizona, our focus has been solely on the general election and preparing for the general election," said Justin Barasky, the super PAC's spokesman. "Nothing that happens in the coming weeks will change our focus from stopping Donald Trump. We expect Hillary to be the nominee."