The dollar rose against most currencies on Monday in thin trading, and held its gains even after President Barack Obama said a deal was in sight to avert a fiscal disaster that would have meant tax hikes and spending cuts for the world’s largest economy.The dollar could come under pressure if a compromise agreement on the U.S. budget is struck as this encourages investors to buy riskier assets, driving flows away from the safe-haven and highly-liquid greenback.Obama said on Monday, the deadline before the U.S. economy goes over the "fiscal cliff”, a deal on the budget was within sight but was not complete yet.His comments bolstered other riskier currencies such as the Australian, New Zealand, and Canadian dollars."Even though, it’s not definitive yet, overall it is hopeful,” said Nick Bennenbroek, head of New York FX strategy, at Wells Fargo in New York"So long as Obama’s statements are consistent with the idea that we are getting a deal, that is going to keep the market relatively calm. That should be positive for foreign currencies because of risk appetite and negative for the dollar as a safe-haven.”He pointed out that Obama’s remarks had limited impact on the currency market only because some participants that could have traded on this news were out of the office.The dollar index was up 0.1 percent at 79.787 .DXY in early afternoon trading. It was down 0.5 percent this year, falling after two straight years of gains.Analysts said Congress could pass legislation in 2013 that retroactively prevents the United States from going over the fiscal cliff, an option that is viewed as politically easier.News reports suggested that the U.S. House of Representatives may not vote on any Senate-passed "fiscal cliff” deal until after Monday’s midnight deadline. A Republican leadership aide that the impact of delaying the vote would be minimal since financial markets would be closed on Tuesday.The euro was down 0.2 percent on the day at $1.3192, with selling accelerated just before the London close. Near-term support was seen around $1.3142, the low set on December 17, according to Reuters data. Any euro gains would be capped at $1.3308, the 8-1/2 month high on December 19, traders said.The euro has gained 1.8 percent against the dollar this year, overcoming worries about a euro zone break-up and any sovereign debt defaults.Sentiment toward the euro improved after the European Central Bank pledged to buy bonds of indebted peripheral countries. Positioning data showed speculators sharply reduced bets against the euro in the week ended December 24.Obama’s statement helped boost the Australian dollar, which rose 0.3 percent to US$1.0403. The U.S. dollar fell 0.4 percent versus the Canadian unit to C$0.9932, while the New Zealand dollar rose more than 1 percent to US$0.8287.