President Obama and former Virginia Gov. Tim Kaine (D) lead their Republican rivals in the key swing state of Virginia, according to a new poll from Quinnipiac University.

Obama leads Mitt Romney by 50 percent to 42 percent and Rick Santorum by 49 percent to 40 percent. Kaine leads former Sen. George Allen (R-Va.) in their Senate race, 47 percent to 44.

Virginia is considered one of the key battleground states next year in both the presidential race and for control of the Senate, and this is the third poll in a row that showed Obama with a significant lead over his rivals.

Adding Virginia Gov. Bob McDonnell (R) as vice president on the Republican ticket does little to help the party's chances, the poll finds: Obama and Vice President Biden would still lead Romney and McDonnell by 50 percent to 43 percent. The poll does not give McDonnell's favorability ratings, but a recent furor over requiring an ultrasound before women could have an abortion might have hurt him in the polls, as the bill was unpopular with Virginia voters.

Kaine's narrow lead over Allen reflects most polls' findings of a tight race between them. He continues to run a few points behind Obama in the state, contradicting many strategists' expectations that he'll run a few points ahead of the president, but that could be because few are paying attention to the Senate race yet, while a negative Republican primary might be hurting the Republican presidential candidates at this point.

The poll of 1,034 registered voters was conducted from March 13 through March 18 and has a margin of error of plus or minus 3.1 percentage points.