President Barack Obama has said he is near the limit on what he can offer to resolve the disagreement while the leader of the opposition, Republican John Boehner, said he will continue to work on a plan.
Talks soured earlier this week after progress was made on taxing and spending cuts. The combination could push the world's largest economy into recession.
"I think the market is having trouble trading the fiscal cliff given the mixture of headlines and uncertainty over any plan," said Win Thin, a currency strategist at Brown Brothers Harriman in New York. "You would think this is dollar positive. Euro still holding up above $1.32, and looks more like a technical bounce."
A U.S. budget agreement is deemed positive for growth-linked currencies such as the euro and Australian dollar, but viewed as negative for the safe-haven dollar. The Republicans announced plans to put an alternative tax plan to a vote in the House of Representatives this week, prompting Democrat Obama to threaten to veto it, thereby unraveling the progress made over the last week.