Christopher C. Healy, the chairman of the Connecticut Republican Party, said Republicans were justified in blocking what he described as a drastic overreaching by Mr. Obama. Still, Mr. Healy acknowledged that Republicans had to be careful about being seen as overly partisan and would now be under increasing pressure to offer a competing vision of governing.

“We can’t be just about saying no,” he said. “But we have not completed the transition yet from defeated incumbent party. We have to position ourselves as an alternative and create enthusiasm for our positions.”

Many of the obstacles facing Republicans were on display in Honolulu. The party chairman, Michael Steele, is an unsettling figure within his own party, as became clear when Ms. Lingle offered a public reprimand to party members for criticizing Mr. Steele, if anonymously, to reporters. “Please don’t do a rebuke in my home state of Hawaii, not to my friend Michael Steele,” she said, as her audience rustled with discomfort.

Republicans have expressed concern about Mr. Steele’s very high profile and often combative style, as well as his propensity to say intemperate things, like predicting that Republicans would not win the majority in the House this November.

Nick Ayers, the executive director of the Republican Governors Association, said he issued a plea similar to Ms. Lingle’s to party members in a private session. He said he was startled at how members were grousing about Mr. Steele, describing it as counterproductive when he was looking to make big gains in races for governor.

For his part, Mr. Steele defended his chairmanship and made clear that he intended to seek re-election when his term ended next year. “My style is not something you get used to very easily,” he said. “I know that.” This took place at a sometimes contentious news conference  “Get your facts right,” Mr. Steele instructed one reporter  that had Republicans wincing at this latest example of Mr. Steele’s sometimes unvarnished ways.

With Mr. Obama seeking to strike a different tone at the beginning of his second year in office, Republicans back in Washington were responding with conciliatory phrases, if not yet substantive compromises.