Young U.S. residents ages 18-29 rank among the least concerned about the potential failure of Congress to strike a deal, with just 56 percent saying they would be personally affected. Only 58 percent of Democrats said the same thing, a stark contrast with Republicans.

The survey comes as President Obama is taking his case on deficit reduction outside Washington. On Monday, Obama visited with auto workers in Michigan, where he pressed his argument that going over the fiscal cliff would hammer working families with an average of $2,200 in new taxes.

Obama has sought to pressure Republicans to only extend the expiring Bush-era tax rates for the middle class. Republicans back extending middle-class rates, but are opposed to tax increases for the wealthy, arguing that the hikes could slow the economic recovery.

Voters surveyed by Gallup are most concerned about the potential that tax levels will increase back to Clinton-era levels across every income bracket, with three-quarters of those surveyed saying that would have a negative impact on their finances. That includes 84 percent of Republicans and 76 percent of Democrats surveyed. 

Just under seven in 10 said major cuts to domestic spending would do the same, while 64 percent said a reduction in the Pentagon's budget could negatively affect their own finances. While 78 percent of Republicans are worried about defense cuts, only 56 percent of Democrats say the same.

"Americans are pretty clear in their views on the fiscal cliff in two respects: they believe the measures would negatively affect the United States as well as their own financial situations, and they want government leaders in Washington to compromise to find an agreement to avoid the fiscal cliff," said Gallup's Jeffrey Jones in a statement.