* Obama to meet congressional leaders at White House
* House of Representatives convenes Sunday on fiscal crisis
* Reid assails Boehner's "dictatorship" in the House
* Tax hikes, spending cuts to begin next week
By Richard Cowan and Mark Felsenthal
WASHINGTON, Dec 27 (Reuters) - President Barack Obama and lawmakers are launching a last-chance round of budget talks days before a New Year's deadline to reach a deal or watch the economy go off a "fiscal cliff."
Obama and Vice President Joe Biden will meet congressional leaders from both parties at the White House on Friday at 3 p.m. EST (2000 GMT) to try to revive negotiations to avoid tax hikes and spending cuts - together worth $600 billion - that will begin to take effect on Jan. 1.
Members were divided on the odds of success, with a few expressing hope, some talking as if they had abandoned it and a small but growing number suggesting Congress might try to stretch the deadline into the first two days of January.
In order to be ready to legislate if an agreement takes shape, the Republican-dominated House of Representatives convened a session for Sunday.
And House Majority Leader Eric Cantor advised members to be prepared to meet through Jan. 2, the final day before the swearing-in of the new Congress elected on Nov. 6.
It "doesn't feel like anything that's very constructive is going to happen" as a result of the meeting with Obama, said Tennessee Republican Sen. Bob Corker. "It feels more like optics than anything that's real."
The two political parties remained far apart, particularly over plans to increase taxes on the wealthiest Americans to help close the U.S. budget deficit. But one veteran Republican, Rep. Jeff Flake of Arizona, held out the prospect that if Obama came through with significant spending cuts, Republicans in the House might compromise on taxes.
The coming days are likely to see either intense bargaining over numbers, or political theater as each side attempts to avoid blame if a deal looks unlikely.
"Hopefully, there is still time for an agreement of some kind that saves the taxpayers from a wholly, wholly preventable economic crisis," Mitch McConnell, the top Republican in the Democratic-controlled Senate, said on the Senate floor.
But the rhetoric was still harsh on Thursday after months of wrangling - much of it along ideological lines - over whether to raise taxes and by how much, as well as how to cut back on government spending.
Senate Majority Leader Harry Reid, the top Democrat in Congress, accused Republican House Speaker John Boehner of running a "dictatorship" by refusing to allow bills he did not like onto the floor of the chamber.
Reid urged Republicans in the House to prevent the worst of the fiscal shock by getting behind a Senate bill to extend existing tax cuts for all except those households earning more than $250,000 a year.
Both Reid and Boehner, as well as McConnell and House Minority Leader Nancy Pelosi, are to meet Obama on Friday.
U.S. stocks sharply cut losses after news of the House reconvening as investors clung to hopes of an 11th-hour deal. Even a partial agreement on taxes that would leave tougher issues like entitlement reform and the debt ceiling until later could be enough to keep markets calm.
"I'm not convinced it will result in a deal, but you could get enough concessions by both parties to at least avoid the immediacy of going over the cliff," said Randy Bateman, chief investment officer of Huntington Asset Management, in Columbus, Ohio.
Obama arrived back at the White House on Thursday from a brief vacation in Hawaii that he cut short to restart stalled negotiations with Congress.
He is likely to meet the toughest resistance from Republicans in the House, where a group of several dozen fiscal conservatives have opposed any tax hikes at all.
But Flake of Arizona said his fellow Republicans in the House and Senate are resigned to seeing some sort of increase in top income tax rates. But they will push back if Obama does not offer spending cuts.
"There will be resistance from a lot of House conservatives to a deal that does that," Flake said.
Strictly speaking, the fiscal cliff measures begin on Jan. 1 when tax rates go up but the House might stay in session until the following day if an agreement is being worked out.
"This January 1 deadline is a little artificial. We can do everything retroactively. We have to get it right, not get it quickly," said Republican Representative Andy Harris.
Another component of the "fiscal cliff" - $109 billion in automatic spending cuts to military and domestic programs - is set to kick in on Jan. 2.
The House and Senate passed bills months ago reflecting their own sharply divergent positions on the expiring low tax rates, which went into effect during the administration of former Republican President George W. Bush.
Democrats want to allow the tax cuts to expire on the wealthiest Americans and leave them in place for everyone else. Republicans want to extend the tax cuts for everyone.
In another sign that Americans are increasingly worrying about their finances as Washington fails to address the budget crisis, consumer confidence fell to a four-month low in December.
Americans blame Republicans in Congress more than congressional Democrats or Obama for the fiscal crisis, a Reuters/Ipsos poll showed.
When asked who they held more responsible for the "fiscal cliff" situation, 27 percent blamed Republicans in Congress, 16 percent blamed Obama and 6 percent pointed to Democrats in Congress. The largest percentage - 31 percent - blamed "all of the above."