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Romney saw a leap in support in the Badger State after Wisconsin Gov. Scott Walker (R) won his recall election there earlier this month. One survey from conservative polling outlet Rasmussen showed Romney moving ahead of Obama 47 to 44.

Many believed the recall election would mobilize and energize the GOP base for the presidential election, but Obama’s lead is now holding steady at 4 points, according to the Real Clear Politics average of polls.

Barack ObamaBarack Hussein ObamaUS set to admit fewest refugees in decades: report NRATV host says Obama owes Parkland students an apology over shooting Paltry wage gains, rising deficits two key tax reform concerns MORE’s the clear favorite to win Wisconsin,” said President of Public Policy Polling Dean Debnam in a statement. “But it looks like it will be a much closer race than his 14 point victory in 2008.” 

Still, Romney has a potential wild card in Wisconsin — if he were to select Rep. Paul RyanPaul Davis RyanScalise released from hospital after planned surgery GOP sold Americans a bill of goods with tax reform law Impeaching Rosenstein? Some Republicans are talking about it MORE (R-Wis.) as his running mate, it would bring him to within 1 point of the president, 47 to 46.

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.

In a conference earlier this month, Republican National Committee Chairman Reince Priebus touted the party’s efforts in Wisconsin, saying that “if Wisconsin goes red, it’s lights out for Barack Obama.”

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

The PPP poll of 1,057 Wisconsin voters was conducted from July 5-8 and has a 3.3 percentage point margin of error.