* Dollar slips, wariness over possible U.S. gov't shutdown * Euro hurt by renewed Italian political tensions * Japan corporate tax-cut hopes lead to yen-selling By Gertrude Chavez-Dreyfuss NEW YORK, Sept 26 (Reuters) - The dollar advanced on Thursday, rebounding from the previous day's losses, after stronger-than-expected U.S. weekly jobless claims data supported a wind-down by the Federal Reserve of its bond-buying stimulus program. The greenback was also helped by the euro's fall on political uncertainty in Italy, the euro zone's third largest economy. But the dollar's gains are expected to be limited as Democrats and Republicans in Congress go down to the wire in budget negotiations to avert a government shutdown on Oct. 1 and raising the federal debt limit, needed to avert a possible federal debt default in mid-October. "The expectation is that tapering will still occur, given the underlying strength in the U.S. economy. The timing of that tapering is still in question, but the direction has never been in doubt," said Lane Newman, director of foreign exchange at ING Capital Markets in New York. On Thursday, data showed the level of initial jobless claims came in much better than expected, with a fall near a six-year low, suggesting a steadily improving labor market. The reading gave a clearer view of the labor market after the number of claims earlier in September may have been distorted as two states updated their their computer systems. In midday New York trading, the dollar was up 0.3 percent against a basket of currencies at 80.563, not that far from a 7-month trough of 80.06 hit on Sept. 18. "The dollar ... found an overall tailwind in unsurprisingly solid news on America's job market, which keeps a Fed taper on the table for possible use in late October," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington. In the bigger picture, the focus shifted back to the U.S. budget fight, which is negative for equities and investments, ING's Newman said. Investors were wary of buying the dollar while the U.S. Congress struggled to avert a government shutdown next week. Still, many analysts believed this would be resolved like previous budget standoffs. The dollar has also struggled since the Fed stunned markets recently by deciding not to scale back its massive stimulus, which raised the question of whether markets have been too optimistic on the U.S. economy. In another criticism about how the Fed handled the decision last week, Fed Governor Jeremy Stein said the U.S. central bank should make itself more predictable about scaling back its stimulus campaign. He maintained the Fed had confused markets by not tapering at its meeting last week. Stein said he would have been comfortable starting to reduce asset purchases at the Sept. 17-18 meeting, and that the decision to keep buying at an $85 billion monthly pace had been, for him, a "close call". The euro fell against the dollar after Italian center-right deputies, supporting former Prime Minister Silvio Berlusconi, renewed threats to resign if their leader is expelled from parliament following a tax fraud conviction. The euro was down 0.3 percent at $1.3485. Against the yen, the dollar was up 0.5 percent at 98.93 yen. The dollar earlier rose as high as 99.13 yen on a media report the Japanese government plans to say it will "urgently consider" cutting the corporate tax rate when it compiles a stimulus package next week. A government source told Reuters last week that Japan will consider cutting corporate taxes and ending a temporary tax hike earlier than scheduled, to cushion the economy from a scheduled sales tax increase. That would add up to more stimulus than previously expected for the economy, which is negative for the yen, helping push Japan's benchmark stock index, Nikkei, higher.