If the 2016 presidential election were held today, former Secretary of State Hillary Clinton might not want to face off against Sen. Rand Paul of Kentucky, according to a new Quinnipiac University Poll of three swing states. Paul is Clinton’s fiercest competition in Colorado, Iowa, and Virginia. Former Florida Gov. Jeb Bush ties her in Virginia and Wisconsin Gov. Scott Walker is in a tie with the former first lady in Colorado.

"Several of the [potential] GOP contenders can take some solace from this poll, although Hillary Clinton remains queen of the public opinion hill at this point,” said Peter A. Brown, assistant director of the Quinnippiac University Poll. “The one GOPer for whom these numbers are a total drag is New Jersey Gov. Chris Christie.”

While Paul may not have tied Clinton in any of the three swing states, his overall numbers were better than Bush and Walker. Clinton led Paul 43 percent to 41 percent in Colorado, 45 percent to 37 percent in Iowa and 44 percent to 42 percent in Virginia. She was ahead of Bush in Colorado 44 percent to 36 percent, and in Iowa 45 percent to 35 percent, but ties him in Virginia with 32 percent each.  She only led Walker, who had the lowest name recognition of any potential 2016 candidate named in the poll, by two percentage points in Colorado. She held a 10-point lead in Iowa and a 5-point lead over the Wisconsin governor in Virginia.

Christie, who is losing popularity in his home state, trails Clinton by nine percentage points in Colorado, 10 points in Iowa and five points in Virginia, the poll showed. Former Arkansas Gov. and Fox News host Mike Huckabee was behind Clinton by six points in Colorado, seven points in Iowa and three points in Virginia.

Voters in the swing states also held it more against Bush that his brother, George W. Bush, and father George H.W. Bush, both served as president over the fact that Clinton’s husband, Bill Clinton, also served as commander-in-chief. Nearly 40 percent of Colorado voters and 35 percent of voters in both Iowa and Virginia said it was less likely they would vote for Jeb Bush because of his family’s ties to the president. But only 24 percent of voters in Colorado, 18 percent in Iowa and 21 percent in Virginia said they would be less likely to vote for Hillary Clinton because Bill was president, the poll found.

"Gov. Jeb Bush has a family problem. Many voters don't like him coming from a family of presidents," Brown said. "If voters are still saying by 4-1 margins this makes them less likely to vote for him when the balloting begins, that will be trouble for him. Few voters, however, say they are put off by Mrs. Clinton being the wife of former President Bill Clinton."

The poll of more than 1,000 voters each in Colorado, Iowa and Virginia was conducted from Feb. 5 to Feb. 15 and has a margin of error of 3 percentage points.