Mr. Cole said Republicans believed the presidential campaign would ultimately motivate their voters and donors and help them oust Democrats who in 2006 gained seats in Republican territories.

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If Senator John McCain of Arizona wins the presidential nomination, Mr. Cole said, that could help Republicans in areas with significant Hispanic populations combined a strong antispending message that appeals to the party’s base.

Mr. McCain is also closely tied to a push for an overhaul of immigration policy that raised the prospect of permanent legal residency for some illegal immigrants. That could dilute the anti-immigration message that House Republicans have seen as one of their most effective weapons.

Mr. Davis is a veteran of the class of 1994 that thrust the Republicans into control of the House. He forged a reputation as an independent while he was the senior Republican on the House oversight committee, occasionally challenging the Bush administration. He represents a suburban district that Democrats view as a seat that could most easily fall in to their hands, along with open districts in Illinois, New Jersey, New York and Ohio.

Mr. Davis said his return to life in the minority party was just one factor in deciding to leave, saying he wanted a sabbatical from politics to look into other opportunities. The congressman, who oversaw the House Republican campaign operation in 2000 and 2002, acknowledged that the landscape for his party was not promising.

“There isn’t any question it is going to be a tough year,” he said.

Four of the 28 Republicans who are so far leaving the House quit before their terms ended. They will be replaced in special elections before November, giving the winners of those races at least the technical mantle of incumbency in the general election.

That leaves 24 open Republican seats, though leaders of both parties expect at least a few more Republican retirements as state filing deadlines arrive. The high point for end-of-session Republican retirements is 27 in 1952, according to Congressional records.