Several Republican presidential candidates are within striking distance of Hillary ClintonHillary Diane Rodham ClintonFive takeaways from Cruz, O'Rourke's fiery first debate Heller embraces Trump in risky attempt to survive in November Live coverage: Cruz, O'Rourke clash in Texas debate MORE in the swing states of Colorado and Virginia, according to a new Quinnipiac University poll released Wednesday. 

Clinton holds at least a 7-percentage-point lead in Iowa against a handful of top Republican contenders, including former Gov. Jeb Bush (Fla.), Sen. Rand PaulRandal (Rand) Howard PaulConservatives left frustrated as Congress passes big spending bills Senate approves 4B spending bill Some employees' personal data revealed in State Department email breach: report MORE (Ky.), Gov. Scott Walker (Wis.) and former Gov. Mike Huckabee (Ark.), but the Democratic front-runner's lead in other states is smaller.

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In Virginia, Bush and Clinton tied at 44 percent support apiece in the poll. Each of the other four Republicans are also within 5 percentage points of Clinton there.

In Colorado, Paul and Walker each trail Clinton by just 2 percentage points, while Huckabee trails Clinton by 5 percentage points.

Paul has perhaps the strongest showing among potential Republican candidates in the poll across all three states, while Christie performed the worst. Walker has the lowest name recognition of the five Republicans, with a majority of voters in each of the three states saying they hadn't heard enough about him. 

More than 7 in 10 voters in each state say Clinton being the first female president if elected wouldn’t impact their vote. 

Clinton's relation to a former president makes less of a difference than Bush's in the poll, with about 6 in 10 voters in each state saying her being married to Bill ClintonWilliam (Bill) Jefferson ClintonTrump, GOP regain edge in Kavanaugh battle Presidential approval: It's the economy; except when it's not Hypocrisy in Kavanaugh case enough to set off alarms in DC MORE makes no difference, while upwards of 16 percent are more likely to vote for her because of it. About 1 in 5 voters said they are less likely to vote for her.

A majority of voters in all three states say Jeb Bush's relation to two former president won't affect their vote, while about a third say it will, and upwards of 9 percent are more likely to vote for him because of it. 

The survey of more than 1,000 voters in each of the three states was conducted Feb. 5-15 via landlines and cellphones with a margin of error of 3 percentage points.