The situation is all the more complicated because, after the party’s defeats in 2008, it has no dominant leaders or cohesive establishment to bridge the divides and help articulate a positive agenda. In that vacuum, the conservative activists and party leaders were both jockeying for advantage on Wednesday.

Mr. Steele, the party chairman, said in an interview that the outcome in New Jersey and Virginia, where Mr. Christie and Mr. McDonnell had played down their conservative views on social issues, instead focusing on the economy, should go a long way toward relieving the divisions and showing the party how to win next year.

Gov. Tim Pawlenty of Minnesota, a potential 2012 presidential candidate who backed Mr. Hoffman in the New York race, told reporters in Iowa that he would not get involved in an intraparty battle again. He said the New York contest, as a special election, had been unusual in that the nominee had been chosen by party leaders rather than by primary.

Mike Huckabee, a former Arkansas governor who is also a possible 2012 contender, urged Republicans not to support third-party candidates, warning that doing so was a recipe for defeat. “There is potential danger if people believe the way to get the attention of Washington is through third-party candidates,” he said. “Typically what a third-party candidate does is ensure the election of the one you like the least.”

But Mr. Huckabee, eager not to alienate conservatives, made clear that he would support primary challenges to Republican candidates who he thought strayed from the party’s values. As one example, he said he was supporting a conservative challenger to Gov. Charlie Crist of Florida, who is seeking the nomination for a Senate seat in a primary that is shaping up as the next big showdown between Republicans.

Senator John Cornyn of Texas, chairman of the National Republican Senatorial Committee, told ABC News that the committee would not spend money on behalf of candidates it is supporting in contested Republican primaries, like Mr. Crist in Florida. Although the committee typically does not spend money in a primary, Republicans said Mr. Cornyn’s remark was intended to relieve some of the anger being directed at the party establishment.