WASHINGTON — President Barack Obama prodded Congress Tuesday to reach a sweeping long-term deal within two weeks to raise the nation’s borrowing limit rather than “kick the can down the road” with a makeshift, short-term solution to stave off a first-ever U.S. default. And he declared the agreement must include the tax hikes Republicans strongly oppose.

Obama said he was summoning leaders of both parties to the White House on Thursday to try to get it done and beat an Aug. 2 deadline to avert a financial crisis that could shake economic markets worldwide.

Republicans sounded entirely unimpressed with Obama’s insistence that the effort include tax increases for the wealthy and narrowed loopholes for oil companies as well as big cuts in government spending.

“We’re not dealing just with talking points about corporate jets or other ‘loopholes,”‘ said House Speaker John Boehner of Ohio. “The legislation the president has asked for — which would increase taxes on small businesses and destroy more American jobs — cannot pass the House, as I have stated repeatedly.”

Boehner said he’d be happy to join discussions at the White House but predicted they “will be fruitless until the president recognizes economic and legislative reality.”

Underscoring the differences, there was even brief discussion about Obama’s claim that progress had been made over the weekend when, as he put it, “my team and I had a series of discussions with congressional leaders in both parties.”

After quick denials from some Republican spokesmen, at first, a congressional official said Boehner and Obama had met Sunday at the White House. That official spoke only on condition of anonymity concerning the private meeting. Obama spokesman Jay Carney declined to provide any details

In his remarks Tuesday, Obama said he strongly opposes a stopgap, short-term debt-limit increase, as suggested by some lawmakers. But he stopped short of ruling out a limited extension, and spokesman Carney later declined to say whether the president would veto such a measure.

Obama renewed his stand that any deal must include not only spending cuts but also new revenue — tax increases vehemently ruled out by many Republicans in Congress.

“We need to come together over the next two weeks to reach a deal that reduces the deficit and upholds the full faith and credit of the United States government and the credit of the American people,” Obama said.

“We’ve made progress, and I believe that greater progress is within sight, but I don’t want to fool anybody — we still have to work through some real differences,” the president said.

He said congressional leaders from the House and Senate, both Republicans and Democrats, were being invited to meet on the issue Thursday at the White House. That would bring the top eight lawmakers together with Obama, Vice President Joe Biden and top administration financial officials.

Obama spoke as the Aug. 2 deadline for raising the nation’s borrowing limit came closer. Experts say lawmakers must waste no time in making a deal if they are to have any chance of getting it finalized and passed through both chambers of Congress in time.

Despite the president’s optimism, it remained unclear where compromise could be found. Republicans are insisting they will note vote to raise the debt limit without major spending cuts; Democrats are refusing to sign off on cuts of such magnitude without at least some tax increases as well. Republicans say they won’t sign off on any tax hikes at all, including those Obama wants targeting the wealthiest Americans or closing loopholes to corporations.

The president called on lawmakers to “leave their ultimatums at the door,” but he stuck to his — that any deal must include new tax revenue. “We need to take on spending in the tax code, spending on certain tax breaks and deductions for the wealthiest of Americans,” Obama said. The White House is proposing about $400 billion in increased tax revenues.

In the Senate on Tuesday, Majority Leader Harry Reid, D-Nev., postponed a test vote on a Libya resolution amid increasing opposition from Republican lawmakers who insisted they should be working on financial security not national security. Several Republican senators had indicated they would oppose using the week debating the Libya measure.

All told, lawmakers and the administration are seeking deficit cuts in the range of $2.4 trillion over the coming decade to balance a similar increase in the debt limit — enough to keep the government afloat past the November 2012 election. Currently the debt limit is $14.3 trillion.

The administration says that if the government’s borrowing limit is not increased by Aug. 2, the U.S. will face its first default ever, potentially throwing financial markets into turmoil.

Many congressional Republicans indicate they’re unconvinced that such scenarios would occur, and some administration officials worry that it could take a financial calamity before Congress acts.

With the deadline nearing, the Senate canceled its July Fourth recess planned for this week.

In discussions led by Vice President Joe Biden that broke off late last month, Republican and Democratic negotiators found more than $1 trillion in potential spending cuts over the coming decade, including reductions favored by both sides.

A Democratic official said last week that of those cuts, roughly $200 billion would come mainly from savings from Medicaid and Medicare, the government health insurance programs for the poor and elderly. Another $200 billion would come from cuts in other automatically paid benefit programs, including farm subsidies. Another large chunk would come from cuts in discretionary spending that Congress approves every year.

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Associated Press writers Julie Pace and Ben Feller contributed to this report.