President Barack Obama said in a speech Wednesday that he thought the budget talks could be resolved in about a week.
The Dow Jones industrial average closed up 83 points at 13,034. It had been up as much as 137 points.
The Standard and Poor's 500 index edged up two points to 1,409. The Nasdaq composite fell 23 points to 2,974, held back by a drop in Apple.
Citigroup jumped 6 percent after the bank said it plans to eliminate more than 11,000 jobs to cut expenses.
Rising stocks narrowly outnumbered falling ones on the New York Stock Exchange. Volume was higher than average at 4.1 billion shares.