Hedge funds were earlier seen buying the euro, which was also helped by the prospect of Italian Prime Minister Enrico Letta's coalition government surviving a confidence vote on Wednesday.
Market participants are now eyeing a European Central Bank policy meeting on Wednesday.
"We do not know how long this impasse in the U.S. will last. If it persists, there is a chance it will hurt economic growth and affect chances of Fed tapering - all of which is dollar negative," said Daragh Maher, strategist at HSBC.
"In the short term, it's better to avoid the dollar."
(Read more: Debt ceiling? The dollar doesn't care)
A potentially bigger political battle looms over raising the U.S. government's borrowing authority. Failure to do so by mid-October could result in a historic U.S. default.
"The U.S will not default because the executive can prioritize debt payments. President Obama would have to choose default, an impossibility," said Joseph Trevisani, chief market strategist at WorldWideMarkets, Woodcliff Lake in New Jersey.
"Markets will assume that the impossible will not happen. But as Oct. 17th approaches market complacency will turn to jitters, especially if there has been no agreement on the budget. No economic good will come out of Washington's politics of mutually assured destruction," he said.
(Read more: US regulators would stop some operations in shutdown)
The dollar's overall weakness gave some reprieve to the yen, which has been under pressure, with the Japanese government on track to raise the national sales tax to 8 percent in April from 5 percent.
To soften the tax's impact, Prime Minister Shinzo Abe said the government will compile an economic stimulus package worth 5 trillion yen in December.
The dollar fell against the yen, losing 0.36 percent to 7.86 yen after earlier falling to 97.64 yen, which was not far from a one-month low of 97.48 yen hit on Monday, according to Reuters data.