Washington (CNN) With the first Democratic debate in the books, a new CNN/ORC poll finds most who watched think Hillary Clinton had the best performance of the night, but her strong showing hasn't boosted her standing in the race for the party's nomination.

Clinton stands at 45% in the race for the Democratic nomination, with Vermont Sen. Bernie Sanders behind her at 29%. Vice President Joe Biden, who is considering a run for presidency and did not participate in last week's debate, follows at 18%.

Behind the top three, former Virginia Sen. Jim Webb had 1% support, while former Rhode Island Gov. Lincoln Chafee, Harvard professor Larry Lessig and former Maryland Gov. Martin O'Malley all held less than 1% support.

Compared with pre-debate polling, Sanders' support is up five points since mid-September, but no other candidate showed significant change.

As Biden mulls whether or not to get in the race, the poll suggests Democrats are becoming less enamored of a run from the vice president. In August, 53% of registered Democrats said they wanted Biden to run, that's down to 47% in the new poll. Should Biden decide to sit out the race for the Democratic nomination, Clinton's lead over Sanders climbs to 23 points: 56% would back Clinton, 33% Sanders.

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

Overall, 31% of registered Democrats say they watched all or most of the CNN/Facebook debate, held October 13 in Las Vegas. More than 6-in-10 Democrats who watched say Clinton did the best job, almost doubling the 35% who thought Sanders had the best performance. On the other side of the coin, 43% of those who watched said Chafee had the worst night, 31% thought Webb did, 12% O'Malley.

Among those Democrats who watched the debate, both Sanders and Biden are viewed more favorably than they are among Democratic voters generally: Sanders' favorability number bumps from 62% among all Democratic voters to 84% among debate viewers, while Biden climbs from 76% to 89% favorable. Clinton's numbers are about the same in both groups.

Despite their positive feelings toward Biden, debate-watchers are more apt than others to say Biden should stay out of the contest (61% think he should not run, compared with 43% of those who did not watch) and they are far more likely to be satisfied with the Democratic field generally (84% compared with 64% among those who didn't watch).

Assessing the lesser-known candidates, debate-watchers are more positive than other Democrats toward O'Malley, (44% favorable compared with 20% among Democratic voters generally). But Webb and Chafee are both viewed more negatively among those who watched (For Chafee, 32% unfavorable among debate-watchers vs. 18% among all Democratic voters; Webb is at 37% unfavorable among debate-watchers, 20% among all Democratic voters).

Following the debate, Clinton continues to dominate as the more trusted candidate across several top issues, with double-digit advantages over Sanders and Biden as the candidate who would best handle the economy, health care, foreign policy, race relations, climate change and gun policy. Clinton also now holds a small edge over Sanders as most trusted on income inequality (43% Clinton, 38% Sanders).

Debate-watchers are more likely than others to say they trust Sanders on top issues, though even among this more-friendly audience, he continues to trail Clinton on most issues. Exceptions are income inequality (50% of debate-watchers trust Sanders vs. 36% for Clinton) and climate change (40% each say Clinton and Sanders would be best able to handle that).

Sanders gained no ground, however, on foreign policy. On that question, Clinton's strength grows among those who watched: 77% in that group say they trust her most to handle foreign policy, up from 66% among Democratic voters overall.

On two issues where the debate highlighted differences among the candidates, fissures within the Democratic electorate on who would best handle them emerge.

Income inequality appears to be the most divisive issue, with women, older voters, those without college degrees, moderates and those with lower incomes more apt to trust Clinton on the issue, while those with college degrees, liberals, and urbanites are more likely to favor Sanders.

And on gun policy, there's a sharp gender divide. Women are far more likely to say they trust Clinton to handle it than men, 50% to 37%. Democratic gun owners are more evenly split on the question, with 35% saying they trust Clinton most on gun policy, 27% Sanders and 21% Biden. Among those Democrats who do not own guns, it's 48% Clinton, 21% Biden and 16% Sanders.

Photos: The first Democratic debate Photos: The first Democratic debate Democratic presidential candidates take the stage before debating in Las Vegas on Tuesday, October 13. From left are former U.S. Sen. Jim Webb, U.S. Sen. Bernie Sanders, former Secretary of State Hillary Clinton, former Maryland Gov. Martin O'Malley and former Rhode Island Gov. Lincoln Chafee. Hide Caption 1 of 10 Photos: The first Democratic debate An audience member watches the debate, which was the first Democratic debate of this election cycle. Hide Caption 2 of 10 Photos: The first Democratic debate Sanders speaks during the debate. CNN's Mark Preston said Sanders' opening remarks "hit on all of the hot-button liberal issues: Take back the government from billionaires, climate change. He all but said it is time for a revolution." Hide Caption 3 of 10 Photos: The first Democratic debate Clinton is the national front-runner in the Democratic race. "I would not ask anyone to vote for me based on my last name," she said during the debate. "I'm campaigning because I think I have the right combination of what Americans are looking for ... and I can take the fight to Republicans." Hide Caption 4 of 10 Photos: The first Democratic debate Webb listens to moderator Anderson Cooper during the debate. Webb is a former Marine who also served as secretary of the U.S. Navy. "You may be sure that in a Webb administration, the highest priority will be the working people who every day go out and make this country stronger at home, and who give us the right reputation and security overseas under a common-sense foreign policy," Webb said. Hide Caption 5 of 10 Photos: The first Democratic debate O'Malley faces the camera while delivering remarks. He went after Sanders on gun control early in the debate, and -- in what could be interpreted as a veiled swipe at Clinton -- he said, "I am very clear about my principles." Hide Caption 6 of 10 Photos: The first Democratic debate Chafee touted his experience, saying he is the only candidate who has been a mayor, senator and governor. "I have had no scandals. I've always been honest. I have the courage to take the long-term view, and I've shown good judgment," he said in his opening statement. Hide Caption 7 of 10 Photos: The first Democratic debate One of the debate's memorable moments was when Sanders and Clinton shook hands following Sanders' take on the Clinton email scandal. "Let me say something that may not be great politics, but the secretary is right -- and that is that 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 8 of 10 Photos: The first Democratic debate Audience members watch the debate. Hide Caption 9 of 10 Photos: The first Democratic debate The Democratic field this year is less than half the size of the Republican field. Hide Caption 10 of 10

Overall, Democrats aren't much more satisfied with their field now than they were in July before any debates had happened. While the share "very satisfied" has risen from 26% to 33%, the share saying they are at least fairly satisfied has held steady at about 7-in-10. Women do report feeling more satisfied with the field than men, but younger Democrats, a key group for Barack Obama's general election victories, are far less satisfied with this field of candidates than older Democrats. Only about one-quarter of those under age 50 say they are very satisfied, compared with 40% of those age 50 or older.

When matched against the top candidates from the Republican field, Clinton, Sanders and Biden all top Donald Trump, who has been leading most polling on the Republican nomination contest since this summer. But Biden is the only one who holds a significant lead over Ben Carson, a more recent addition to the top of the Republican field. Trump trails Clinton by 5, Sanders by 9 and Biden by 10. But against Carson, both Clinton (47% to Carson's 48%) and Sanders (46% to Carson's 48%) run about evenly with the former neurosurgeon. Biden tops Carson by 8 points.

The CNN/ORC International Poll was conducted by telephone October 14-17 among a random national sample of 1,028 adult Americans. Results among the 425 registered voters who say they are Democrats or independents who lean toward the Democratic Party have a margin of sampling error of plus or minus 5 percentage points.