The GOP used the threat of a government shutdown in April to cut 2011 spending and threatened to allow the U.S. to default on its obligations in August unless a debt-reduction plan was enacted.
The final cuts and debt plan nonetheless disappointed fiscal conservatives.
Obama has countered the GOP strategy by insisting the party is protecting the wealthy while slashing aid to the poor and to the elderly.
The Pew survey finds two-thirds of those surveyed support increasing taxes on the wealthy to balance the budget, while 55 percent oppose cutting poverty programs such as Medicaid.
This week, House Republicans and Senate Democrats are battling over disaster aid as the clock ticks down to the end of the fiscal year on Oct. 1 without an overall spending bill in place.
Pew interviewed 1,000 adults from Sept. 22 through Sept. 25.