Romney edges Obama 48 percent to 47, according to the poll, which has a 4.5 percent margin of error. Obama led Romney 49 to 46 percent in the previous Rasmussen poll, taken in July.

Obama still leads by 4.3 percent in Wisconsin, according to the Real Clear Politics average of polls, although most of the data contributing to that average is from before the state's gubernatorial recall election in June.

The Rasmussen survey is the first Badger State poll to be released since Romney announced Wisconsin Rep. Paul RyanPaul Davis RyanThree House Dems say they'll oppose immigration floor vote over possible wall funding Dems after briefing: 'No evidence' spy placed in Trump campaign Senate approves new sexual harassment policy for Congress MORE (R) as his running mate. Rasmussen found Ryan to be hugely popular in his home state, with 57 percent saying they have a favorable view of him, against only 36 negative.

This is not the first time in this election cycle the right-leaning pollster has found a swing in support in Wisconsin after a significant political event. Obama led Romney 49 to 44 percent in Wisconsin in May, according to Rasmussen, but Romney swung to a 47 to 44 percent lead after Wisconsin Gov. Scott Walker (R) won his recall election.

Obama held leads of between 5 and 7 percentage points in Wisconsin, according to three major polls conducted just before the addition of Ryan to the GOP presidential ticket. One of those polls, a survey from liberal-leaning Public Policy Polling released in July, showed Obama with a 6-percentage-point advantage in Wisconsin, but had Romney pulling to within 1 point with the addition of Ryan to the ticket.

Wisconsin is one of 12 battleground states — the others are Michigan, Florida, North Carolina, Virginia, Colorado, Nevada, New Mexico, Iowa, Ohio, Pennsylvania and New Hampshire — that will be critical in determining the outcome of the 2012 election.

Wisconsin hasn't backed a Republican for president since Ronald Reagan in 1984.