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Mr. Herron is in a tight race with Republican Steve Fincher for the rural west Tennessee seat, where Mrs. Pelosi is unpopular even among many Democrats.

“The people of my district are independent-minded folks who put patriotism above partisanship and are not looking to hire a yes man for either party,” Mr. Herron said. “I will not vote for John Boehner or Nancy Pelosi to serve as speaker of the House.”

Alabama’s Mr. Bright last week became the first House Democrat to say that he definitively won’t vote for Mrs. Pelosi as speaker should both return to the 112th Congress.

“I am not going to vote for Nancy Pelosi as speaker of the House. Neither the leader of the minority party, John Boehner, nor the present speaker, will get my vote,” Mr. Bright told Montgomery TV station WSFA. “I will vote for someone, a centrist, who is much more like me.”

Rep. Peter A. DeFazio, a liberal Oregon Democrat who has clashed with Mrs. Pelosi, also has signaled he may not back her for another term as speaker.

Despite some Democrats’ reluctance to embrace Mrs. Pelosi, the Californian has raised more than $217 million for Democrats since she entered leadership in 2002, a senior Democratic aide said. She has held 212 political events in 24 states and one territory since last year, excluding events in her home San Francisco district and Washington, D.C.