CONCORD, N.H. — The awards ceremony Friday evening for New Hampshire’s police forces was full of pomp, circumstance, officers in dress uniforms and a show of support from the state’s full congressional delegation.

But almost as soon as all the awards had been given and the photos taken, New Hampshire’s four members of Congress, three of them Democrats, were set upon by local reporters with one simmering question: What are you going to do about the faltering Affordable Care Act?

Rep. Ann McLane Kuster, the state’s freshman Democrat, displayed her own exasperation over the failed rollout. “Patience is a virtue, and Americans have it in short supply,” she said. “Frankly we are not well served by the politics of all this.”

For Democrats across the country, the reversal of political fortunes over the past month has been head-spinning. In mid-October, as Republicans were contending with voter fury over a 16-day government shutdown, Democrats had the momentum. Polls showed a growing number of voters who said they wanted the party to control Congress after next year’s election.

Then the problems with the Internet-based health exchanges came into focus, followed by millions of letters from insurance companies canceling individual policies that did not meet the health law’s minimum coverage requirements. Republicans found their voice. Democrats lost theirs. The polling gap closed, and Republican wallets opened. The National Republican Senatorial Committee raised $3.8 million in October, its best monthly showing of the year.

New Hampshire’s two House members, Kuster and Carol Shea-Porter, are facing combative Republican challengers and a wave of caustic attacks over the health law. Both broke rank with their leaders and the White House on Friday, voting for a Republican bill to reinstate insurance policies that had been canceled for failing to meet minimum standards set by the Affordable Care Act, and to let insurance companies enroll more people in such plans.

Friday’s 261-157 House vote on the Republican bill included a roster of 39 Democrats.

For Democrats, voting for Republican health care bills may not be a political panacea. After Friday’s vote, the National Republican Congressional Committee mocked vulnerable Democrats who voted yes as political turncoats. Shea-Porter, the New Hampshire congresswoman, said she understood that — and had no intention of playing down her support for the health law.

“I’m very proud that I voted for it, and I think all the kinks will be worked out,” she said. “In the interim, this is what I believe in. I just have to keep working.”