WASHINGTON (AP) -- The White House and Republican congressional leaders made significant progress late Saturday toward a deal to avert a government default threatened for early next week, according to officials familiar with the talks.

Under the plan, the nation's debt limit would rise in two steps by about $2.4 trillion and spending would be cut by a slightly larger amount, the officials said. The first stage _ about $1 trillion _ would take place immediately and the second later in the year.

Congress would be required to vote on a balanced budget amendment to the Constitution, but none of the debt limit increase would be contingent on its approval.

The officials who described the talks did so on condition of anonymity, citing their sensitive nature.

President Barack Obama is seeking legislation to raise the government's $14.3 trillion debt limit by enough to tide the Treasury over until after the 2012 elections. He has threatened to veto any legislation that would allow a recurrence of the current crisis next year but has agreed to Republican demands that deficits be cut _ without tax increases _ in exchange for additional U.S. borrowing authority.

Without a compromise in place by Tuesday, administration officials say the Treasury will run out of funds to pay all the nation's bills. The subsequent default could prove catastrophic for the U.S. economy by causing interest rates to rise and financial markets to sink, sending shockwaves around the world, they say. With financial markets closed for the weekend, lawmakers had a little breathing room, but not much. Asian markets begin opening for the new work week when it is late Sunday afternoon in the U.S. capital.

``There is very little time'' Obama said Saturday in his weekly radio and Internet address. He called for an end to political gamesmanship, saying ``the time for compromise on behalf of the American people is now.''

One official commenting on the late night negotiations said the two sides had settled on general concepts, but added there were numerous details to be worked out _ and no assurance of a final agreement.

Still, word of significant progress after weeks of stalemate offered the strongest indication yet that an economy-crippling default might be averted.

Democratic Senate Majority Leader Harry Reid postponed until Sunday a test vote on a his own debt limit proposal that had been scheduled for shortly after midnight to give negotiators time to work out an agreement.

``There are many elements to be finalized,'' he cautioned. ``There is still a distance to go.''

Senate Republican leader Mitch McConnell said at a joint news conference with House Speaker John Boehner earlier that he was confident a deal could be reached ``in the very near future and resolve this crisis in the best interests of the American people.''

Reid, after a meeting at the White House with Obama and House Democratic leader Nancy Pelosi, disagreed with that optimistic assessment.

Obama needs Congress to approve an increase in the government's borrowing authority, known as the debt ceiling. Past increases have been routine, but Republicans, citing the giant U.S. deficit, have demanded huge spending cuts as a condition for approving the increase.

After weeks of intense partisanship, there was renewed talk of compromise that contrasted sharply with earlier developments as both the House and Senate convened for unusual Saturday sessions.

McConnell and Boehner held their news conference shortly after the House of Representatives rejected a Senate Democratic bill drafted by Majority Leader Harry Reid to raise the government's debt limit by $2.4 trillion and cut spending by $2.2 trillion.

The House vote was 246-173, mostly along party lines and after debate filled with harsh, partisan remarks. The vote was unusual in that Republicans lined up to kill Reid's legislation even though it hadn't even cleared the Senate. It was orchestrated as political payback because late Friday Reid had engineered the demise of a House-passed bill hours after it passed.

Shortly after the House vote, Obama stepped back into the debt-ceiling talks, calling Democratic leaders Reid and Pelosi to the White House for a meeting.

Before the House vote, Republicans said the Reid spending-cuts plan was filled with gimmicks and would make unacceptable reductions in defense spending.

Pelosi said Boehner ``chose to go to the dark side'' when he changed his own legislation to satisfy tea party-backed Republican lawmakers and other critics, prompting catcalls from the Republican side of the aisle.

Not even Democrats seemed to like Reid's measure very much, although many emerged from a closed-door meeting of the rank and file saying they would vote for it.

With their votes, many Democrats signaled their readiness for compromise by voting to cut spending without raising taxes. Many Republicans insist taxes must not be raised to cut into federal deficits, even for the wealthiest Americans and for big oil companies.

There was no doubt about the outcome of Sunday's planned procedural vote in the Senate, either, unless compromise intervened. A total of 43 Republicans sent Reid a letter saying they would block the bill from advancing, enough to prevent it from coming to a final vote under Senate rules.