Before the release of Mr. Ryan’s proposal, Republicans had expressed confidence that public opinion had turned in their favor, and on Tuesday House leaders sought to reassure Republicans that their budget approach would eventually carry the day. Led by Speaker John A. Boehner of Ohio, Republicans held a conference call urging House members to tell voters that it is the Obama administration’s spending plan that would cost jobs and ration health care.

Officials familiar with the call said that rank-and-file lawmakers did not seem alarmed at the response they were getting, and that Mr. Ryan told his fellow Republicans he had been successful in making the case that Medicare would go bankrupt without intervention. Mr. Ryan said he stressed with his constituents that those over 55 or currently on Medicare would still be covered under the existing program.

But news reports noted that Mr. Ryan himself faced a mixed response Tuesday as he held tense meetings with voters, some of whom were turned away because of overflow crowds. It was another indication that Republicans still have a big selling job to do on their budget, especially to older constituents who tend to turn out to vote at higher rates than younger people.

“I think what we have in Washington right now working on Medicare are a bunch of clowns,” said Robert Murphy, 73, a retiree in Fort Lauderdale. “I think they should leave Medicare alone. But I know they can’t leave it the way it is.”

At Mr. West’s meeting on Tuesday evening here, he took only written questions submitted by the audience. The queries were largely friendly, but some people did pipe up loudly about Medicare, accusing him of making misleading remarks. Several were escorted out by security.

Democrats and their allies are stepping up their efforts to organize opposition at public events. They hope to put Republicans back on their heels much as Republicans did to Democrats in the angry town-hall-style meetings conducted during consideration of the health care law.

“We have said from the moment the gavel came down on the vote to end Medicare we would hold them accountable every day in every way,” said Representative Steve Israel of New York, chairman of the Democratic Congressional Campaign Committee. “That is precisely what we are doing. We encourage everyone to attend these meetings.”