But in Florida, where Irma left more than a dozen dead and millions without electricity, a handful of Republicans have been more outspoken. The Republican mayor of Miami, Tomás Regalado, urged Mr. Trump last week to reconsider his climate policies. Several Florida lawmakers founded a bipartisan Climate Solutions Caucus in the House of Representatives, and the group’s Republican membership grew this year to two dozen.

The safe ground for Republicans, party strategists say, may be embracing proposals to mitigate certain effects of environmental change, while skirting debate about more drastic actions that experts see as essential.

That approach reached even the White House this week, with Thomas P. Bossert, Mr. Trump’s Homeland Security adviser, declaring that the administration takes “seriously the threat of climate change.” He added, somewhat vaguely, “Not the cause of it, but the things that we observe.”

Representative Scott Taylor of Virginia, a Republican whose district hugs the Atlantic Coast, said his constituents were growing more sensitive to the implications of climate change, including voters who lean to the right. Mr. Taylor, who is a member of the climate caucus, said he was still wary of hobbling fossil-fuel companies, but favors narrower measures to address dangerous environmental conditions. The Republican nominee for governor of Virginia this year, Ed Gillespie, has taken a similar tack, ignoring climate as an issue but releasing a plan on coastal flooding.

“We have to deal with issues like sea-level rise and flooding and resiliency,” Mr. Taylor said, cautioning, “I don’t think we’re there, in a bipartisan way, for comprehensive action.”

Jay Faison, a wealthy Republican donor who has made clean energy a personal cause, said he found Republicans increasingly open to engaging around the edges of the climate issue. Mr. Faison said he had reason to believe there was “some appetite” among congressional leaders for backing resilient infrastructure and energy research.

“I’d like to see more, faster,” Mr. Faison said. “But we play the hand we’re dealt.”

Political polling has long found most voters sympathetic to policies that protect the environment, including the Paris agreement and rules proposed by the Obama administration to curb power-plant emissions. But Americans have also tended to rank climate low among their priorities, behind issues like health care and jobs.