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 RyanElection Countdown: Trump confident about midterms in Hill.TV interview | Kavanaugh controversy tests candidates | Sanders, Warren ponder if both can run | Super PACs spending big | Two states open general election voting Friday | Latest Senate polls On The Money: Midterms to shake up House finance panel | Chamber chief says US not in trade war | Mulvaney moving CFPB unit out of DC | Conservatives frustrated over big spending bills Nancy Pelosi: Will she remain the ‘Face of the Franchise’? 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.