US President Barack Obama and legislators are set to launch 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 Joe Biden, the vice-president, were expected to meet congressional leaders from both Democrat and Republican parties at the White House on Friday to try to revive negotiations to avoid tax hikes and spending cuts - together worth $600bn - that will begin to take effect on January 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 January 2, the final day before the swearing-in of the new Congress elected on November 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 Senator 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 US budget deficit. But one veteran Republican, 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 theatre as each side attempts to avoid blame if a deal looks unlikely.