President Barack Obama leads presumptive GOP presidential nominee Mitt Romney in Wisconsin in the first major poll of Badger State voters since Rep. Paul Ryan was added to the Republican ticket.

Forty-nine percent of likely Wisconsin voters said they would vote for Obama if the election were held today, versus 46 percent of voters who said they would vote for the Romney-Ryan ticket, according to a Marquette University Law poll released Wednesday.

That's a much closer margin than has separated Romney and Obama in this swing state for much of 2012; the two candidates were tied in Marquette's likely voter model in mid-May, but Obama opened a wider lead over Romney during the course of the summer. The law school's last poll conducted before the Ryan pick had Obama ahead, 50-45 percent.

NBC News currently rates Wisconsin a "toss up" in its ratings of swing states this fall. But no Republican presidential candidate has won there since President Ronald Reagan in 1994. Nonetheless, the GOP ticket did campaign there shortly after Ryan was named Romney's running mate, and some Republican super PACs have spent on television advertising in the state.

To that end, 29 percent of registered Wisconsin voters said the choice of Ryan made them more likely to vote for Romney, and 13 percent said it would make them less likely to support the former Massachusetts governor. But 53 percent said Ryan's addition to the GOP ticket had no impact on their vote.

**Also of note: Former Wisconsin Gov. Tommy Thompson, on the heels of his victory this month in a three-way Republican primary, leads Democratic Rep. Tammy Baldwin in the race for Wisconsin's open Senate seat.

Fifty percent of registered Wisconsin voters said they would vote for Thompson, versus 41 percent who would back Baldwin. Both are running to succeed retiring Democratic Sen. Herb Kohl.

The poll, conducted Aug. 16-19, has a 4.2 percent margin of error for its sample of likely voters, and a 3.8 percent margin of error for its sample of registered voters.