As liberals overwhelm congressional town hall-style meetings and deluge the Capitol phone system with pleas to protect the health law, there is no similar clamor for dismantling it, Mr. Obama’s signature legislative accomplishment. From deeply conservative districts in the South and the West to the more moderate parts of the Northeast, Republicans in Congress say there is significantly less intensity among opponents of the law than when Mr. Obama was in office.

“I hear more concerns than before about ‘You’re going to repeal it, and we’re all going to lose insurance’ because they don’t think we’re going to replace it,” said Representative Mike Simpson, a Republican who represents a conservative district in Idaho…

“I was here in 2009 and 2010, and we’re not getting the anti-Obamacare calls like that,” said Representative Brett Guthrie, a Kentucky Republican who is on one of the committees tasked with rewriting the law. “I think people are going to hold us accountable for making sure we not only repeal, but we have a law in place that creates a better opportunity for people.”

The demands from conservative-leaning constituents in districts like Mr. Guthrie’s are plainly shifting. In a nationwide CBS News poll last month, 53 percent of Republicans said they wanted to change the law to make it work better while 41 percent said they wanted to abolish it.