A new Quinnipiac poll of swing states Florida, Ohio and Pennsylvania shows that Vice President Joe Biden would do better than Democratic frontrunner Hillary Clinton in certain 2016 general election matchups.

Clinton is still beating Biden handily in polls of Democratic primary voters. But in certain hypothetical general election matchups Biden has a stronger lead against potential Republican challengers -- or beats them where Clinton cannot.

In Florida, Biden would beat Republican frontrunner Donald Trump 45 to 42, whereas Clinton would lose to Trump 43 to 41. Both Clinton and Biden would lose to former Florida Gov. Jeb Bush and Florida Sen. Marco Rubio, two other Republican candidates.

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In Ohio, both Biden and Clinton beat Trump -- but Biden has a 10-point margin over Trump, compared to Clinton's five-point margin. Clinton would also beat Bush and Trump but lose to Rubio, whereas Biden would beat all three.

And in Pennsylvania -- the state where Biden was raised -- he would beat Trump 48 to 40, versus Clinton's lead of 45 to 40. Bush and Rubio would beat both Clinton and Biden there.

"Vice President Joseph Biden, who is spending his time in seclusion, contemplating whether to take on Secretary Hillary Clinton in the Democratic primaries for president, has some new information to consider," Peter Brown, assistant director of the Quinnipiac University Poll, said in a news release about the poll. The vice president hasn't yet decided whether to run again for the Democratic nomination, but would likely need to enter the race within the next few weeks in order to have enough time for fundraising and developing a ground organization.

Quinnipiac also tested how Trump could affect the race if he runs as an independent. Republicans fear an independent Trump bid would hand the election to Hillary Clinton - this poll will not ease those fears.

In Florida, Bush would beat Clinton by 11 points if they were the only two candidates. Add Trump to the mix and he loses by 1 percent while Trump brings in 19 percent of the vote. In Ohio, Clinton's 2-point lead becomes a 10-point lead over Bush, with Trump bringing in 23 percent of the vote -- just 4 percent less than Bush. And in Pennsylvania, Bush goes from leading Clinton by 3 points to losing to her by eight points while Trump gets nearly a quarter of votes.

Clinton and Biden are both leading their respective primary contests, but in all three states more voters give them a negative favorability rating than those who give them a positive rating. They also get the lowest ratings on honesty and trustworthiness. Biden, on the other hand, has better scores on honesty and trustworthiness and more voters rating him as favorable than not.

"Hillary Clinton's poll numbers are like a leaky faucet: drip...drip... drip. She is now getting less than half the vote in all three states' Democratic primaries," Brown said. "The good news for Clinton is that she remains far ahead of U.S. Sen. Bernie Sanders of Vermont and Biden in the three Democratic primary contests."

The Florida and March primary contests don't happen until March 15, meaning voters may not be paying much attention to the election just yet, so the poll at this point may reflect name recognition. Pennsylvanians won't go to the polls until April 26.

Quinnipiac polled just over 1,000 voters in each of the three states and all three have a margin of error of plus or minus 3 percentage points. The interviews were conducted on land lines and cell phones.