* Consumer confidence rebounds in November * Home prices fall 0.6 pct in Sept, 1.2 pct in 3rd quarter * Number of 'underwater' borrowers declines in 3rd quarter * Chain store sales rise in latest week By Leah Schnurr NEW YORK, Nov 29 (Reuters) - Americans shook off some of their concerns about the economy this month but a surprise fall in house prices in September underscored the weak foundations of the recovery. Consumer sentiment rebounded in November from a 2-1/2-year low last month and U.S. retailers reported strong sales as the holiday shopping season got off to a positive start last week. The Conference Board said on Tuesday its index of consumer attitudes jumped to 56.0 from 40.9 in October, hitting the highest level since July and handily topping economists' forecasts for 44.0. "This is a huge rise in consumer confidence. It gets us back to second-quarter levels and further underscores the dramatic move that we've seen in consumer spending," said Lindsey Piegza, economist at FTN Financial in New York. Still, the confidence index remains historically low and is well below a recent peak of 72.0 in February. Americans worried less about jobs and their income. A measure of how hard jobs are to get fell to its lowest since January 2009 at 42.1 percent. Expectations of income increases in the next six months rose to 14.9 percent from 11.1 percent. Consumer confidence took a hit in recent months after political gridlock in August pushed the United States close to a debt default, worries grew about another U.S. recession and the euro zone debt crisis deepened. The cutoff date for the latest survey was Nov. 15, before the failure of a congressional committee charged with tackling the U.S. budget deficit. While fears of recession have ebbed, analysts warn the economy remains sensitive to shocks, particularly the risk of fallout from the euro zone debt crisis. "It's a conflicted environment," said Paul Ballew, chief economist at Nationwide Insurance in Columbus, Ohio. "The underlying readings on the U.S. recovery are a bit stronger than what some people feared, but that's offset by the looming concerns of what we're seeing in the headlines and what's playing out primarily in Europe." The sentiment data helped push U.S. stocks higher, while fears over Europe moderated for the time being and investors dipped back into risky assets. Euro zone ministers on Tuesday were expected to approve detailed plans to bolster their bailout fund to help prevent contagion in bond markets.As the housing market struggles to recover, the large number of homeowners who are underwater has prompted concerns of more foreclosures to come if borrowers become unable to keep up with their payments or decide to walk away.