Rep. Michele Bachmann is Minnesota Republicans’ choice to take on Democratic Sen. Amy Klobuchar in 2012, according to a new survey from the Democratic-leaning firm Public Policy Polling.

But the poll found Klobuchar would defeat any of the high-profile Republicans who were tested. No Republican has announced intentions to oppose Klobuchar yet. PPP surveyed 387 Republican primary voters on Dec. 4 and 5. The poll had a margin of error of 5 points.

Bachmann got the support of 36 percent of Republicans. She was easily elected to a third term in a district northwest of the Twin Cities in 2010, and her strong fundraising, rising national profile and the possibility that Minnesota may lose a House seat have prompted speculation that she might run for higher office. The broader survey of 949 Minnesota voters found Klobuchar beat Bachmann, 56 percent to 39 percent. It had a margin of error of 3.2 points.

Outgoing Gov. Tim Pawlenty, often discussed as a potential presidential candidate, got the support of 20 percent of Republican primary voters. He did better against Klobuchar: The survey found he trailed her by 10 points. Former Sen. Norm Coleman, who lost to Democratic Sen. Al Franken in 2008 and now leads the American Action Network, got 14 percent of Republicans’ support and lost to Klobuchar by 14 points.

The rest of the potential Senate candidates finished in the single digits. In descending order they were Rep.-elect Chip Cravaack with 7 percent, former gubernatorial candidate Tom Emmer with 6 percent, Rep. John Kline with 5 percent, outgoing state Rep. Laura Brod with 4 percent and Rep. Erik Paulsen with 2 percent.

Klobuchar, a former Hennepin County attorney, was first elected in 2006 when she defeated Republican Rep. Mark Kennedy. She got 58 percent of the vote in that race.