Senate due to vote at 1800 BST on compromise thrashed out over weekend before plan passes to House of Representatives

Congress and the White House were closing in on a deal on Sunday to head off huge market falls and the prospect of America defaulting on Tuesday for the first time in its history.

The Senate is scheduled to vote around 1pm (1800 BST) on a compromise thrashed out over the weekend between the Democratic leader in the Senate, Harry Reid, and his Republican counterpart, Mitch McConnell.

McConnell, interviewed on CNN on Sunday, said: "We are very close. We had a good day yesterday. Both the president and vice-president called me … and they understand we have to come together."

The deal would then have to go to the House of Representatives, which could be more problematic given the Republican majority.

There are enough mainstream Republicans, when combined with Democrats, to pass the bill and that is likely to happen. But the Republican House speaker, John Boehner, will be uneasy about alienating the large core of hardline conservatives, mainly Tea Party sympathisers, who will probably vote against it, and may seek last-minute concessions to try to pacify them.

According to officials familiar with the talks, a plan negotiated late on Saturday night would see the ceiling would be raised in two steps by about $2.4tn (£1.5tn) and spending would be cut by a slightly larger amount. The first stage – to raise the ceiling by about $1tn – 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 rise would be contingent on its approval.

President Barack Obama is seeking legislation to raise the government's $14.3tn debt limit by enough to tide the US treasury over until after the 2012 elections. He has threatened to veto any proposals that might lead to a recurrence of the current crisis next year but has agreed to Republican demands that deficits be cut – without tax increases – in exchange for authorising additional US borrowing.

Without a compromise in place by Tuesday, administration officials say the treasury will run out of funds to pay the nation's bills.

The subsequent default, which would be the first in US history, could prove catastrophic for the US economy by causing interest rates to rise and financial markets to sink, and sending shockwaves around the world. With financial markets closed for the weekend, the parties to the talks had a little breathing space, but not much. Asian markets open for the new working week late Sunday afternoon, Washington time.

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

Past increases in the US debt ceiling have been routine, but Republicans, citing the giant US deficit, have demanded huge spending cuts as a condition for approving the increase this time.