WASHINGTON - The Republican defeat in a special congressional contest in Mississippi sent waves of apprehension across an already troubled party on Wednesday, with some senior Republicans urging congressional candidates to distance themselves from President Bush to head off what could be catastrophic losses in the fall.

The victory Tuesday by Travis Childers, a conservative Democrat elected in a once-steadfastly Republican district, was the third defeat of a Republican in a special congressional race this year. In addition to foreshadowing more losses for the party in November, the outcome appeared to undermine the idea that Sen. Barack Obama could be a liability for other Democratic candidates in conservative regions.

Republicans had sought to link Childers to Obama in an advertising campaign there. Republican leaders said they were looking toward Sen. John McCain of Arizona, the likely Republican nominee, as a model whose independent reputation appears to allow him to rise above party in a year when the Republican label seems tarnished.

But McCain's advisers said the Mississippi race underlined his intention to distance himself as much as possible from congressional Republicans. McCain has already been openly critical of some of President Bush's strategies.

The level of distress was evident in remarks by senior party officials throughout the day.

"This was a real wake-up call for us," Robert Duncan, the chairman of the Republican National Committee, said in an interview. "We can't let the Democrats take our issues. We can't let them pretend to be conservatives and co-opt the middle and win these elections. We have to get the attention of our incumbents and candidates and make sure they understand this."

Rep. Thomas M. Davis III, R-Va., a former leader of his party's congressional campaign committee, issued a dire warning that the Republican Party had been severely damaged, in no small part because of its identification with Bush. Davis said that, unless Republican candidates moved dramatically, they could lose 20 seats in the House and six in the Senate.

"They are canaries in the coal mine, warning of far greater losses in the fall, if steps are not taken to remedy the current climate," Davis said in a memorandum. "The political atmosphere facing House Republicans this November is the worst since Watergate and is far more toxic than it was in 2006."

The result in Mississippi, and what Republicans said was a surge in African-American turnout, suggested that Obama might have the effect of putting into play Southern seats that were once solidly Republican, rather than dragging down congressional candidates.

GOP leaders under pressure

At a tense, private post-mortem Wednesday morning, worried House Republicans demanded that their leadership come up with a plan to stave off potentially devastating losses in November. Republican officials said no leaders or top campaign strategists appeared to be in immediate danger of losing their positions, though in interviews, there was evidence of vast dissatisfaction, frustration and discouragement with the party's position.

"The Republican brand is down, and it is going to be hard to get it back," said Rep. Devin Nunes, R-Calif.

Rep. Peter T. King, R-N.Y., said it appeared that lawmakers might have to fend for themselves. "You are going to have to run on who you are and establish some independence, and that is going to be tougher for some than others," King said.

Rep. Tom Cole of Oklahoma, the chairman of the National Republican Congressional Committee, did not go as far as his predecessor, Davis, in advising members to step away from Bush.

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