WASHINGTON — President Barack Obama declared today that Congress has a “unique opportunity to do something big” and stabilize the U.S. economy for decades by cutting deficits even as it raises the national debt limit ahead of a critical Aug. 2 deadline. He said was willing to make tough decisions himself, including trimming Medicare benefits for wealthy beneficiaries, but said, “We’re running out of time.”

Obama challenged Republican lawmakers to make tough calls, too. He attempted to turn their opposition to any tax increases back against them, warning starkly that failure to raise the debt ceiling would mean “effectively a tax increase for everybody” if the government defaults, sending up interest rates.

Still, Obama said that “it’s hard to do a big package” in deadlocked Washington. He said of the Republicans: “If they show me a serious plan I’m ready to move.”

The president spoke at the White House today after five days straight of meetings with congressional leaders failed to yield compromise — amid increasingly urgent warnings from credit agencies and the financial sector about the risks of failing to raise the government’s borrowing limit.

Administration officials and private economists say that if the U.S. fails to raise its borrowing limit and begins to stop paying its bills as a result, the fragile U.S. economy could be cast into a crisis that would reverberate around the globe. Democratic and Republican congressional leaders agree on the need to avert that outcome, but that hasn’t been enough to get Republicans to agree to the tax hikes on corporations and the wealthy sought by Obama — or to convince Obama and Democrats to sign onto the steep entitlement cuts without new revenue that Republicans favor.

In a light moment on a day heavy with economic concern, Obama was asked why he still had hopes that the White House negotiations would provide any results, given the lack of success so far.

“I always have hope,” he said with a smile. “Don’t you remember my campaign?”

It was his third news conference in two weeks on an issue that is increasingly consuming Washington and his presidency.

The president said he was ready to make tough decisions such as restructuring Medicare so that very wealthy recipients would have to pay slightly more. “Things like that would be appropriate,” he said. “That could make a difference.”

He said he had stressed to Republicans that anything they looked at should not affect current beneficiaries, and he said providers such as drug companies could be targeted for cuts. The president wouldn’t comment when asked whether he would support raising the Social Security retirement age.

On Capitol Hill, meanwhile, Democrats and Republicans in the House emerged from closed-door meetings to reiterate their hardened stances. Republicans announced plans to call a vote next week on a balanced budget constitutional amendment that would force the government to balance its books.

Obama dismissed the idea, saying, “We don’t need a constitutional amendment to do that. What we need to do is do our jobs.”

Failure to reach compromise has focused attention on a fallback plan under discussion by Senate Republican leader Mitch McConnell and Senate Majority Leader Harry Reid. That plan would give Obama greater authority to raise the debt ceiling while setting procedures in motion that could lead to federal spending cuts.

Obama insisted the public was on his side in wanting a “balanced approach” that would mix spending cuts and the tax increases opposed by Republicans.

“The American people are sold,” he said. “The problem is that members of Congress are dug in ideologically.”

He renewed his pitch for a major package of some $4 trillion, about three-quarters of which would be spending cuts along with about $1 trillion in new revenue.

“We have a chance to stabilize America’s finances for a decade or 15 years or 20 years if we’re willing to seize the moment,” the president said, adding later that everyone must be “willing to compromise.”

“We don’t need more studies, we don’t need a balanced budget amendment,” Obama said. He said lawmakers simply needed to be able to make tough decisions and stand up to their political bases.

Meanwhile the administration dispatched Treasury Secretary Tim Geithner and Budget director Jacob Lew to meet with House Speaker John Boehner and Majority Leader Eric Cantor at the Capitol.

Even as he prodded Republicans, Obama also issued a challenge to his liberal base, saying progressives should be just as interested in solving the country’s debt and deficit woes as conservatives.

“It would be very helpful for us to be able to say to the American people, ‘Our fiscal house is in order and now the question is what should we be doing to win the future?'” the president said, saying that otherwise investments such as more spending on community colleges could be dismissed as “more big spending, more government.”

“The American people do not want to see a bunch of posturing. They don’t to hear a bunch of sound bites. What they want is for us to solve problems. And we all have to remember that. That’s why we were sent here.”

The outline of the McConnell plan was winning unusual bipartisan support even as some conservatives voiced misgivings.

Under the plan, which would require approval by the House and Senate, Obama would have the power to order an increase in the debt limit of up to $2.5 trillion over the coming year unless both the House and Senate voted by two-thirds margins to deny him. Reid and McConnell were trying to work out ways to guarantee that Congress would also get to vote on sizable deficit reductions. The plan also could be linked to immediate spending cuts already identified by White House and congressional negotiators.

Obama offered measured praise: “It is constructive to say that if Washington operates as usual and can’t get something done let’s at least avert Armageddon.”

But the president said that McConnell’s approach only addressed the pressing issue of the debt ceiling, not the country’s longer-term deficit woes, and he wanted to handle that as well.