WASHINGTON — The signal of the presumptive Republican presidential nominee, Senator McCain, that he may be open to a higher payroll tax for Social Security, despite previous vows not to raise taxes of any kind, is drawing sharp rebukes from conservatives.

Mr. McCain’s shift has come in stages, catching some Republicans by surprise. Speaking with reporters on his campaign bus on July 9, he cited a need to shore up Social Security. “I cannot tell you what I would do, except to put everything on the table,” he said.

He went a step farther Sunday on ABC’s “This Week,” in response to a question about payroll tax increases.

“There is nothing that’s off the table. I have my positions, and I’ll articulate them. But nothing’s off the table,” Mr. McCain said. “I don’t want tax increases. But that doesn’t mean that anything is off the table.”

That comment drew a strong response this week from the Club for Growth, a Washington anti-tax group. Mr. McCain’s comments, the group said in a letter to the Arizona senator, are “shocking because you have been adamant in your opposition to raising taxes under any circumstances.”

Indeed, Mr. McCain frequently has promised not to raise taxes.

At a July 7 town-hall meeting in Denver, he said voters faced a stark choice between him and Senator Obama.

“Senator Obama will raise your taxes,” Mr. McCain said. “I won’t.”

In a March 16 interview with Fox News’ Sean Hannity, Mr. McCain said he would cut taxes where possible, and not raise them.

“Do you mean none?” Mr. Hannity asked.

“None,” Mr. McCain replied.

Both candidates have said Social Security’s funding formula needs to be changed to ensure the program’s long-term viability. Mr. Obama has called for imposing a new payroll tax on incomes above $250,000. Currently, only incomes up to $102,000 are subject to the 12.4% payroll tax, which employers and employees split evenly.

When Mr. Obama announced his plan June 13, Mr. McCain’s top economic adviser, Douglas Holtz-Eakin, told reporters that as president, Mr. McCain would not consider a payroll tax increase “under any imaginable circumstance.”

Mr. McCain has made no specific proposals for Social Security, refusing to rule in or out anything to strengthen the benefit program for retirees and the disabled. Both candidates have said that, if elected, they would try to work out details with Republican and Democratic lawmakers.

Asked for an explanation of Mr. McCain’s latest comments, a campaign spokesman, Tucker Bounds, said the Arizona senator “has a clear and demonstrated record of opposing tax increases. John McCain is going to cut taxes” and improve government discipline, he said.

Promises never to raise taxes have bedeviled past Republican officeholders. Before being elected in 1988, President George H.W. Bush said, “Read my lips, no new taxes.” But facing severe budget problems, he reneged on the promise. Some conservative groups never forgave him.