Washington ? President Barack Obama and congressional leaders on Monday emerged still deeply divided over how to slash the nation’s debt, with reality sinking in that even a middle-ground proposal was not big enough to succeed and would not get through Congress anyway.

As time runs perilously short for action, Obama challenged top lawmakers to return to the White House today with fresh ideas for a debt-reduction plan that could pass the House and Senate. All sides are scrambling to reach a deal as part of a tradeoff in which Congress would agree to extend the nation’s debt limit by Aug. 2 to prevent a catastrophic government default on its bills.

Turning up the pressure, Obama declared that he would reject any stopgap extension of the nation’s borrowing limit, imploring lawmakers once again to reach one of the most sizable debt-reduction deals in years.

He refused to even entertain a backup plan if that doesn’t happen.

“We are going to get this done,” Obama insisted in a news conference.

In a 90-minute closed meeting, House Majority Leader Eric Cantor spelled out potential spending cuts that had been identified in talks led for weeks by Vice President Joe Biden. But Democratic lawmakers in the room made clear such a cutting-only approach without tax hikes on wealthier Americans would never pass the Democratic-led Senate or the House, where Democratic votes would be needed, too.

It did not appear, either, that such a plan would meet the House Republicans’ own standard of a debt-cutting package. They want cuts that would exceed the size of the increase in the debt limit, which could be about $2.4 trillion to get the country through 2012 and next year’s elections.

Republicans won’t support a package that raises any taxes.

As the stalemate continues, the pressure increases. A government default could trigger another enormous economic swoon.

Democratic officials familiar with the White House position in the private talks insist that leaders of the House and Senate will not let that happen, and that Republicans ultimately would vote to raise the debt limit even if a deficit-cutting package does not come together in time.

Yet Republicans say otherwise. House Speaker John Boehner insists the House can’t pass such a bill.

“I agree with the president that the national debt limit must be raised, and I’m glad that he made the case for it today,” Boehner told reporters. “But the American people will not accept – and the House cannot pass – a bill that raises taxes on job creators.”

Obama renewed his case for a package that would put a historic dent in the country’s deficits by blending politically poisonous elements for both parties: tax hikes for the wealthy and big corporations opposed by Republicans and social service cuts that Democrats decry.

He implored both political parties to give ground and show the American people that Washington can actually work.

“If not now, when?” Obama said.