The senators who brought down their party’s push to repeal the Affordable Care Act do not appear eager to kill the party’s last, and only, hope for a legislative accomplishment this year. And for all their posturing, naysayers on the particular tax bill pending before the Senate have pressed for a way forward.

“It’s one of those things that’s hard to articulate, but the mood is very different,” said Senator James E. Risch, Republican of Idaho. “People really want to get to yes.”

Hurdles do remain, and the effort to satisfy some reluctant senators could anger other senators who like the bill as it is. About half a dozen Republicans, including Senators Ron Johnson of Wisconsin and Bob Corker of Tennessee, have expressed various degrees of misgivings about the tax bill, like the way it treats small businesses and its effect on an already large and growing budget deficit.

But the differences between the health and tax debates have been striking.

President Trump, who was largely disengaged from the health bill debate — he called the House’s version of repeal “mean” after celebrating its passage in the Rose Garden — has shown deeper interest in the tax overhaul. During a lunch with Senate Republicans on Tuesday, he “got pretty deep in the weeds,” Mr. Risch said.

Another big difference: Unlike the tax measure, the health bill did not go through what the Senate calls “regular order,” with a formal bill drafting in the relevant committees. That created a kind of free-for-all atmosphere in which senators who have little expertise in health care fancied themselves experts and put forth proposals that were destined to fail, said Senator Roy Blunt, Republican of Missouri.

“I think there’s a reason you have these committees of expertise,” Mr. Blunt said. “A lot of the questions that would never have been answered if you had gone through the outrageous process we went through on health care can get answered, because the people who have been working on it know the answers.”