Perhaps most significant, Republicans have begun to acknowledge the depth of public concern about efforts to dismantle the Affordable Care Act, a shift that could affect the prospects of their long-promised repeal. At a raucous town hall, Senator Tom Cotton of Arkansas, a fierce critic of the law, allowed that the measure “has helped many Arkansans.”

Senator Charles E. Grassley of Iowa said it was clear that the party had to proceed with care. “There’s more of a consensus among Republicans now that you got to be more cautious what you’re going to do,” he said after one spirited event.

Other Republicans worried that their peers were beginning to lose their nerve.

“There are, in my opinion, a significant number of congressmen who are being impacted by these kinds of protests, and their spine is a little bit weak,” Representative Mo Brooks of Alabama told a local radio station. “And I don’t know if we’re going to be able to repeal Obamacare now, because these folks who support Obamacare are very active. They’re putting pressure on congressmen, and there’s not a countereffort to steel the spine of some of these congressmen in tossup districts around the country.”

Mr. Schumer noted that just weeks ago Senate Republicans had hoped to pick off red-state Democrats in their effort to overhaul the health care system. That talked has faded, at least somewhat.

He placed the odds of the health care law’s survival at “significantly greater than 50 percent.”

Looking further ahead, leaders of the Democratic Party, eager to harness the energy they have done little to generate themselves, say they are seeing uncharacteristic constituent interest in local races — including among citizens hoping to run as candidates themselves — at every level.

The Democratic Congressional Campaign Committee said it had held more than 100 “meetings or serious conversations” with potential recruits for the 2018 cycle. Since January, the group said, 1.2 million new people had been added to an online donor list.