CBS News said 44 percent of respondents expect time will run out before a deal is made.The budget cuts and tax hikes are effective Jan. 1.
CBS said 58 percent of Democrats think a deal will be made compared to 38 percent of Republicans.
Although all parties involved are receiving criticism, CBS said the public is more critical of the Republicans in Congress, with 69 percent disapproving of their actions compared to 50 percent disapproving of the president and congressional Democrats.
The survey found that 69 percent of those asked support raising taxes on those with household incomes of $250,000 and higher.
But CBS did say wide political differences remain, with 84 percent of Democrats supporting raising taxes on higher income households and 51 percent of Republicans favoring the same measure.
There are also large differences on cutting government spending, with 58 percent of Republicans favoring cuts and 60 percent of Democrats opposing them.
2014: The Year in Music [PHOTOS]