* Spanish, Italian bonds benefit from better risk appetite * Italian yields back at pre-Monti resignation plan levels * Bunds ease, look prone to further falls By William James and Marius Zaharia LONDON, Dec 18 (Reuters) - Spanish and Italian bonds rallied on Tuesday as progress in U.S. budget talks and the absence of any fresh domestic scares lifted investor demand for higher-yielding assets and weighed on safe-haven Bunds. The prospect of a series of painful automatic austerity measures in the United States next year dimmed slightly when, according to a source familiar with the talks, President Barack Obama made a counter-offer to Republicans that included a change in position on tax hikes for the wealthy. That prompted a rally in equities globally and the desire to secure investment returns pushed some back towards the euro zone's lower-rated peripheral bonds as the effects of last week's political shock in Italy subsided. That narrowed the yield differential with German debt. "Certainly one thing that's clear is that news in the U.S. is getting better and better," DZ Bank strategist Christian Lenk said. "Everybody is looking for yield these days, if you want to have something in the euro zone you will buy Spain and Italy. Maybe the lack of bad news is sufficient for some investors to buy them." Spanish debt extended gains after Madrid's final bill sale of the year raised more than the target amount. There are no long-term peripheral debt sales due until Italy sells bonds on Dec. 28 and the lack of supply was also supportive, traders said. Spanish 10-year bond yields fell 12 basis points to 5.33 percent while the equivalent on Italian debt fell 11 bps to 4.46 percent. Italian yields moved back below levels seen before Prime Minister Mario Monti sparked a wave of selling last week after announcing he would resign early. Investors have since bought back into Italy on the view that any successor government would remain committed to Monti's reform agenda. A POSITIVE SPIN The shift towards riskier assets spurred some investors to trim their holdings of low-risk debt such as U.S. Treasuries and German Bunds - assets used as hedges that should rally if the U.S. budget talks do not produce a deal. Bund futures were 47 ticks lower on the day at 144.36, while 10-year cash yields were 4.1 basis points higher at 1.412 percent. The break through 144.54, the 62 percent Fibonacci retracement of the November-to-December rally opened the way towards 143.53, the lows seen late last month, according to Richard Adcock, a technical strategist at UBS. DZ Bank's Lenk said the technical picture for Bunds suggested there was potential for further falls. The session lows have been falling for the past six sessions, including on Tuesday. Budget talks in the United States may weigh on Bunds if successful, but a sharp, sustained falling trend is unlikely. A grim global economic outlook for next year was expected to bring in buyers on any price dips. "The market is trying to get a positive spin on things at the moment. It shows that people want to believe," said Peter Allwright, head of absolute return on rates and currency at RWC Capital Markets. "But there's still going to be some tightening. It's still going to be a source of contraction, even if they do a deal."