Tea-party activists, keen to build on their success toppling GOP incumbents in primaries this year, are already targeting more Republican veterans in the 2012 election.

Sen. Olympia Snowe of Maine, one of the most liberal Republicans in Congress, already has a conservative GOP primary opponent. Sen. Orrin Hatch (R., Utah), Sen. Bob Corker (R., Tenn.) and Sen. Richard Lugar (R., Indiana) have all drawn fire from the right wing of their party.

Tea-party...