WRAPUP 8-U.S. heading off 'fiscal cliff' despite Senate efforts
* "Fiscal cliff" tax hikes, spending cuts loom
* White House and Senate agree to New Year's Eve deal
* U.S. House members have left for the night
WASHINGTON, Dec 31 (Reuters) - The United States was headed over the "fiscal cliff" - at least temporarily - at midnight on Monday as time was running out for lawmakers to back a last-minute deal between the White House and Senate leaders to avert severe tax increases and spending cuts.
After months of fruitless argument between Republicans and Democrats, the White House and Senate reached an agreement that would delay harsh spending cuts by two months, administration sources said.
The Senate might hold a rare New Year's Eve vote on the plan worked out between Biden and Republican Minority Leader Mitch McConnell, but the House of Representatives is unlikely to get around to it until Tuesday at the earliest.
That would mean Congress failed to meet its own deadline to avert t he "fiscal cliff," some $600 billion of tax hikes and spending cuts due to kick in on Tuesday.
The fiscal measures could push the U.S. economy into recession and roil global financial markets. But the damage would not be severe if lawmakers can at least finalize a deal in the coming days.
House approval is unsure as many of the Republicans who control the chamber complain that President Barack Obama has shown little interest in cutting government spending to try to reduce the U.S. budget deficit.
House Republicans are also likely to balk at planned tax hikes on the wealthy that were part of the agreement negotiated by Biden.
As New Year's Day approached, members were thankful that financial markets were closed, giving them a second chance to return on Tuesday to try to blunt the worst effects of the fiscal mess.
Despite the New Year's Eve deadline, there is no major difference whether a law is passed on Monday night, Tuesday or Wednesday. Legislation can be backdated to Jan. 1, for instance, said law firm K&L Gates partner Mary Burke Baker, who spent decades at the Internal Revenue Service.
"This is sort of like twins and one being born before midnight and one being born after. I think the date that matters is the day president signs the legislation," she said.
House Republicans wished each other "Happy New Year" and left the Capitol building, but their leaders told them to avoid too much New Year partying and be available for a vote on Monday night if needed.
"We were encouraged to stay close to the Capitol and in a good state of mind," said Representative Steven LaTourette of Ohio.
The House was to convene on Tuesday at noon (1700 GMT).