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Other potential tea party pickups include an empty seat in closely divided Wisconsin, where Sen. Herb Kohl, a Democrat, is retiring.

The Club for Growth, the influential anti-spending group, as well as Sens. Jim DeMint of South Carolina and Mr. Paul already have embraced the candidacy of former Rep. Mark Neumann, a tea party favorite who lost his 2010 gubernatorial primary bid to Scott Walker.

Mr. Neumann faces state Assembly Speaker Jeff Fitzgerald and former Wisconsin Gov. Tommy G. Thompson, who has faced stiff criticism over statements he has made in support of Mr. Obama’s health care overhaul.

The jury, though, is still out on the level of influence the tea party movement will have in the coming elections, where the stakes will be higher as Mr. Obama fights for his political survival.

The list of potential targets seems to have already dwindled, with tea partyers conceding that it could be hard to oust such veterans as Sens. Olympia J. Snowe of Maine and Orrin G. Hatch of Utah.

Mrs. Snowe has been helped enormously by an endorsement from Gov. Paul LePage, who won the state’s top office with tea party support. Mr. Hatch, who has moved to the right in recent years, also dodged a bullet when Rep. Jason Chaffetz announced in August that he would not challenge the 36-year incumbent.

Tea party groups are also split over whom to support in the Nebraska primary for the seat being vacated by Sen. Ben Nelson, a Democrat. Some are lining up behind state Treasurer Don Stenberg, and others backing state Attorney General Jon Bruning.

Mark J. Rozell, professor of public policy at George Mason University, said that the 2010 election was probably the “peak” of the tea party movement and that by the end of 2012, “we’ll all be talking again about how the movement contributed positively to some GOP campaigns and then relegated other Republicans to defeat.”

He also noted that the different structural conditions of the 2012 race likely will weaken tea party impact.

“The movement had a big impact in a lower-turnout midterm election cycle, under conditions ideally suited to a committed minority of voters. Even under those conditions, tea party insistence on ideological purity consigned the GOP to defeat in some very winnable Senate campaigns,” he said.

“For 2012, the movement’s impact will be diluted by higher voter-turnout rates and the probable lack of a genuine tea partyer as the GOP presidential nominee. Whether [Mitt] Romney or even [Newt] Gingrich, I don’t see the top of the GOP ticket anchoring tea party enthusiasm.”

A Pew Research poll, meanwhile, also shows that compared with 2010, the movement has become better known and less popular, both nationally and in congressional districts represented by tea-party-backed members.

But David Kirkham, co-founder of the Utah Tea Party and potential challenger to the state’s Republican governor, shrugged off the findings.

He said “our greatest hope” is that the political world “underestimates our resolve to get responsible and accountable government.”

“We are not going anywhere,” Mr. Kirkham said, adding that his group has been working behind the scenes in Utah to turn state lawmakers against immigration-reform legislation providing guest-worker status for undocumented immigrants and to repeal a rollback of Utah’s open-records laws.

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