Washington (CNN) The stakes of Bernie Sanders' take-it-to-the-convention strategy are rapidly rising as fresh polls underscore Hillary Clinton's vulnerabilities and predict a tight race between her and Donald Trump in the fall.

After months of talk about the potential of a contested Republican convention, Trump, the presumptive GOP nominee, is quickly consolidating his party's support -- something Clinton is unable to do with Sanders still in the race.

With only a few major nominating contests left, including California and New Jersey on June 7, Sanders lacks a credible mathematical path to overhauling Clinton's wide lead in pledged delegates. And with polls showing Clinton's general election advantage over Trump evaporating, a lingering fracture in the Democratic party could be perilous for its chances to keep the White House.

Still, Sanders is not heeding calls from some Democrats to get out of the race -- or at least cool his rhetoric during the final weeks of the primary season. Instead, he kept up his blistering criticism of Clinton over the weekend and deepened his feud with the party establishment, including endorsing the primary challenger to Democratic National Committee Chairwoman Debbie Wasserman Schultz.

"The last I heard is that we are a democratic country, and that elections are about vigorous debates over the issues. Secretary Clinton and I disagree," Sanders told Jake Tapper Sunday on CNN's "State of the Union." "What the Democratic leadership has got to understand is that not all of my supporters go to these fancy fundraising dinners. They're working people who are hurting now, who want real change in the economy."

He added: "I hope the Democratic leadership understands they have to open up the process, bring those people in."

'Uphill fight'

Sanders acknowledged in the interview that he has a "very, very uphill fight" in his quest to overtake Clinton, given that he has won 46% of pledged delegates so far and she has won 54%. But he rebuked Democratic superdelegates -- party office holders and lawmakers who can vote however they choose at the convention -- for overwhelmingly coming out for Clinton early on in what he said was an "anointment" by the establishment and big money interests.

Clinton's failure to finally put away the Sanders campaign is grating on the former secretary of state.

"I will be the nominee for my party,'' Clinton told CNN's Chris Cuomo in an interview last week. "That is already done, in effect. There is no way I won't be.''

Photos: Hillary Clinton's life in the spotlight Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 1 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 2 of 43 Photos: Hillary Clinton's life in the spotlight Rodham was a lawyer on the House Judiciary Committee, whose work led to impeachment charges against President Richard Nixon in 1974. Hide Caption 3 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 4 of 43 Photos: Hillary Clinton's life in the spotlight Arkansas' first lady, now using the name Hillary Rodham Clinton, wears her inaugural ball gown in 1985. Hide Caption 5 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons celebrate Bill's inauguration in Little Rock, Arkansas, in 1991. He was governor from 1983 to 1992, when he was elected President. Hide Caption 6 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 7 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 8 of 43 Photos: Hillary Clinton's life in the spotlight During the 1992 presidential campaign, Clinton jokes with her husband's running mate, Al Gore, and Gore's wife, Tipper, aboard a campaign bus. Hide Caption 9 of 43 Photos: Hillary Clinton's life in the spotlight Clinton accompanies her husband as he takes the oath of office in January 1993. Hide Caption 10 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons share a laugh on Capitol Hill in 1993. Hide Caption 11 of 43 Photos: Hillary Clinton's life in the spotlight Clinton unveils the renovated Blue Room of the White House in 1995. Hide Caption 12 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 13 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons hug as Bill is sworn in for a second term as President. Hide Caption 14 of 43 Photos: Hillary Clinton's life in the spotlight The first lady holds up a Grammy Award, which she won for her audiobook "It Takes a Village" in 1997. Hide Caption 15 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 16 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 17 of 43 Photos: Hillary Clinton's life in the spotlight The first family walks with their dog, Buddy, as they leave the White House for a vacation in August 1998. Hide Caption 18 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 19 of 43 Photos: Hillary Clinton's life in the spotlight Clinton announces in February 2000 that she will seek the U.S. Senate seat in New York. She was elected later that year. Hide Caption 20 of 43 Photos: Hillary Clinton's life in the spotlight Clinton makes her first appearance on the Senate Environment and Natural Resources Committee. Hide Caption 21 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 22 of 43 Photos: Hillary Clinton's life in the spotlight Clinton holds up her book "Living History" before a signing in Auburn Hills, Michigan, in 2003. Hide Caption 23 of 43 Photos: Hillary Clinton's life in the spotlight Clinton and another presidential hopeful, U.S. Sen. Barack Obama, applaud at the start of a Democratic debate in 2007. Hide Caption 24 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 25 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 26 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, as secretary of state, greets Russian Prime Minister Vladimir Putin during a meeting just outside Moscow in March 2010. Hide Caption 27 of 43 Photos: Hillary Clinton's life in the spotlight The Clintons pose on the day of Chelsea's wedding to Marc Mezvinsky in July 2010. Hide Caption 28 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 29 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 30 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 31 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 32 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 33 of 43 Photos: Hillary Clinton's life in the spotlight Clinton, now running for President again, performs with Jimmy Fallon during a "Tonight Show" skit in September 2015. Hide Caption 34 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 35 of 43 Photos: Hillary Clinton's life in the spotlight 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." Hide Caption 36 of 43 Photos: Hillary Clinton's life in the spotlight Clinton is reflected in a teleprompter during a campaign rally in Alexandria, Virginia, in October 2015. Hide Caption 37 of 43 Photos: Hillary Clinton's life in the spotlight Clinton walks on her stage with her family after winning the New York primary in April. Hide Caption 38 of 43 Photos: Hillary Clinton's life in the spotlight 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." Hide Caption 39 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 40 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 41 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 42 of 43 Photos: Hillary Clinton's life in the spotlight 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. Hide Caption 43 of 43

On Sunday, she said there will be an "obvious need of us to unify the party" once she becomes the presumptive nominee.

"I will certainly do my part, reaching out to Sen. Sanders, reaching out to his supporters," she said on NBC's "Meet the Press." "And I expect him to do his."

The internal conflict comes at a time when polls show that Trump is getting a dividend from closing out the Republican primary race, and setting up what could be a close election against Clinton in November.

A CNN/ORC poll from the beginning of May found Clinton leading Trump by 13 points. But in more recent surveys, there is increasing evidence of a bump in polling as Trump consolidates GOP support.

A Fox News poll last week showed Trump leading Clinton 45% to 42%, findings that were within the survey's margin of error. Meanwhile, a New York Times/CBS News national survey released Thursday had Clinton up by six points.

Washington Post/ABC News poll Sunday found a statistical dead heat, with Trump leading Clinton 46% to 44% among registered voters, figures that represent an 11-point swing since March. The former secretary of state leads by six points among all adults -- down from an 18-point lead in March.

Quinnipiac University polls in swing states Ohio, Florida and Pennsylvania this month also had the rivals effectively neck-and-neck.

Polls this far out from a general election cannot offer a reliable picture of what will happen in November. But they can shape the political environment in which the early stages of the race evolves and, if they continue to show Trump gaining in strength, are likely to increase pressure on Sanders to bring the Democratic Party together.

But Sanders does not see such polls as an argument that he should get out of the race or dial back attacks on Clinton. In fact, he sees them as proof that he would be a superior general election candidate to the former first lady -- most polls show him leading Trump.

'I have been vetted'

In the NBC interview, Clinton suggested Sanders simply hasn't been subjected to the rough and tumble of politics the way she has.

It's "fair to say that I have been vetted and tested, and I think that that puts me in a very strong position," she said.

Referring to Sanders, she said, "let me say that I don't think he's had a single negative ad ever run against him."

Sanders disputed the notion that he is only doing better than Clinton because he has not had to endure the years of partisan warfare that have shredded her approval ratings.

"Any objective assessment of our campaign versus Clinton's campaign, I think, will conclude we have the energy, we have the excitement, we have the young people, we have the working people, we can drive a large voter turnout, so that we not only win the White House, but we retain, regain control of the Senate, do well in the House and in governor's chairs up and down the line," Sanders told Tapper.

Latest polls clearly show that the lingering Democratic Party divisions are a challenge for Clinton.

The Washington Post/ABC poll released Sunday showed that in a match-up equation with Trump, Clinton currently gets 86% of Democratic voters, meaning that a slice of the party coalition that is not yet sold on her as nominee.

Making a decision to leave a primary race or to tone down attacks on a rival who appears headed for victory is the toughest choices any candidate faces. It is a particularly acute dilemma for Sanders, given that he has won millions of votes, ignited a populist uprising in the Democratic Party that no one saw coming and is basking in an unprecedented reception to his democratic socialist ideas that left him in the political wilderness for years in the Senate.

He and his campaign team have dismissed the idea that he could wreak lasting damage on Clinton if she becomes the nominee, saying he will do whatever it takes to ensure that Trump does not win the presidency. But if his arguments about the process of the Democratic primary race leave the impression that he has been unfairly treated and that Clinton is somehow not the legitimate nominee, the task of uniting the party becomes far more difficult.

Sanders vs. DNC

That's where Sanders' clash with Wasserman Schultz is particularly concerning to some Democrats. The Vermont senator's campaign has consistently accused the DNC chairwoman of tilting the race in favor of Clinton and criticized the scheduling of debates on Saturday nights when television audiences are lower, and the closed primaries that bar independents in big states like New York.

Sanders is now backing Wasserman Schultz's primary opponent in her Florida district, Tim Canova, and left no doubt about the strengths of his feelings about her on Sunday.

"Well, clearly, I favor her opponent," Sanders told Tapper. "His views are much closer to mine than as to Wasserman Schultz's." "In all due respect to the current chairperson. If (I was) elected president, she would not be reappointed to be chair of the DNC."

Sanders campaign manager Jeff Weaver also sent out a fundraising email to supporters Sunday seeking contributions for Canova.

For all the sudden handwringing in Democratic circles, it's still likely that Clinton will enjoy her own boost in the polls once she finally becomes the presumptive Democratic nominee similar to the one Trump is enjoying now.

For now, veteran Democrats appear to be ready to give Sanders some room. But the clock is ticking.

"After (Clinton) has actually won, after she actually has enough delegates to win the nomination, I think Bernie needs to think about his legacy," said Mark Alderman, a top Democratic Party donor who was part of President Barack Obama's transition team. "Bernie is in the middle of the tsunami -- he doesn't have any perspective yet. It will take a little time. Unfortunately, he only has a little time. He has got to get it together by July."