Republican leaders are still calling for major changes in entitlement programs — despite vociferous criticism from Democrats and some interest groups — as they start to spell out their conditions for raising the debt ceiling.

On Thursday, Senate Minority Leader Mitch McConnell called for a system of spending caps for discretionary and entitlement accounts to be put in place over the next five to 10 years as part of a deal to raise the $14.3 trillion debt limit.

The Kentucky Republican indicated he was referring to Medicare and Medicaid, while conceding that Social Security would not be included in the negotiations. He also refused to consider tax increases.

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House Speaker John A. Boehner, R-Ohio, also has called for major alterations to entitlement spending, suggesting the two parties are headed for a showdown over the two health care programs. Democrats have staunchly defended Medicare in the past, and they are likely to redouble those efforts with an eye toward the 2012 elections.

When asked what changes he wants attached to an increase, Boehner suggested “budget process reforms” such as “real program changes that will put these entitlement programs on a much stronger foundation where they can be preserved for the tens of millions of Americans who count on them.”

It remains unclear, however, how much leverage Republicans hold in the debate and whether they can extract entitlement cuts opposed by Democrats and still rule out tax increases.

The White House says taxes should be part of the negotiations — and it appears confident that Republicans will not, in the end, prevent a debt ceiling increase, given the damage a default would do to the economy.

Still, some in the GOP are warning that lawmakers should ready themselves for a bumpy debate, with the possibility of multiple, short-term debt limit increases, particularly because House Republicans are reluctant to vote for large debt ceiling increases.

“Because there is a limit to how much debt the House would even consider, I believe we have to plan for multiple debt limit bills — giving us the chance to attach multiple anti-spending reforms to any new debt,” Sen. Mark Steven Kirk, R-Ill., said.

While Democrats consistently have attacked House GOP proposals to transform Medicare into a voucher-like program, President Obama concedes the need to curb the growth of federal health care spending.

On the other side, Boehner already has called for trillions of dollars in spending cuts in return for supporting an increase in the government’s borrowing capacity. The Speaker’s proposed reductions would far outpace the increase in the debt limit.

Still, Boehner was cagey about specifics, saying he will not agree to “phony caps” — perhaps reflecting the fact that members of his caucus are still proposing and debating a variety of spending curbs.

And there were other signs of potential compromise. During a Thursday meeting with Senate Republicans, Obama endorsed working with governors to find a way to control Medicaid costs.

Sen. John Hoeven, R-N.D., a former governor, urged Obama to consider the effect of rising Medicaid costs on state budgets.

“The fastest growing driver of the states’ expenses is Medicaid,” Hoeven said. Obama responded by suggesting working with the National Governors Association on “solutions for Medicaid that will help the states.”

“The president brought that up,” Hoeven said. “That’s a very good idea. We need to work with those governors.”

In a rare news conference, McConnell described what he said were his own conditions for raising the debt limit. He started with caps on non-emergency discretionary spending over the next two years.

For the medium term, or the next five or 10 years covered in a congressional budget “window,” McConnell said there should be caps on entitlement spending as well as discretionary.

He was more vague about long-term changes he is seeking.

“We all know that long-term we have over $50 trillion in unfunded liabilities in very popular programs that Americans depend on — Medicare, Social Security, Medicaid — that are simply on an unsustainable path,” he said.

McConnell’s embrace of spending caps suggests that an effort to mandate spending limits without specifying where cuts would be made is in play in GOP negotiations over the debt limit.

Bob Corker, R-Tenn., is hoping a spending cap plan (S 245) he and Claire McCaskill, D-Mo., introduced could be a vehicle for raising the debt ceiling. Their bill would limit total government spending, including Social Security, to a historical level of 20.6 percent of gross domestic product. If Congress did not adhere to that limit, across-the-board spending cuts automatically would go into effect.

McConnell did not bring up the Corker-McCaskill legislation as an example of the kind of cap mechanism he favors. However, the minority leader supports the legislation, a spokesman said. Boehner has not said he opposes spending caps.

Republicans have ruled out anything like Obama’s proposed debt trigger, which would require automatic cuts in spending and reductions in tax breaks if the debt did not stabilize and show signs of shrinking as a share of the economy by 2014.

“Some have suggested that we use triggers. Mr. President, the triggers have already been pulled,” McConnell said in a floor speech. “What good is a fire alarm that goes off after the building burns down? Agreeing to a trigger is to deny this crisis.”

GOP leaders also want the next budget caps to have real teeth.

“I don’t want to tie myself down in terms of what those are but I don’t want phony caps,” Boehner said. “We know all the gimmicks that have been used in the past have never worked. Congress has found a way to wiggle out of all of them.”

Obama and many Democrats contend that increased revenues have to be part of the solution to the nation’s budget woes.

Conceding that he was initially skeptical of Obama’s call for a face-to-face with Senate Republicans, McConnell said it turned out to be “a very good meeting” and that the need to raise the debt limit provides a rare opportunity for the two parties to strike a deal.

While touting the bipartisan panel of lawmakers led by Vice President Joseph R. Biden Jr., as the best hope for reaching an agreement on the debt limit, McConnell also gave credit to the president’s 2010 fiscal commission for its deficit reduction recommendations.

“All the options are on the table, thanks to the president’s deficit reduction commission,” he said. “It’s a question of what do you want to pick up and do.”

Paul M. Krawzak and Joseph J. Schatz writes for CQ. Brian Friel contributed to this story.