The new poll found that, by 46 percent to 30 percent, more favor cutting government services to raising taxes to tackle budget deficits. That sentiment echoes the view of the GOP, which has emphasized spending cuts during four years of budget battles with Obama.
Yet support for trimming government services has dropped in AP-GfK polls. It was 56 percent last February and 62 percent in March 2011.
Still, Ray Wilkins, 58, of Belton, Mo., a warehouse worker, said, "The government's gotten too big. The federal government tries to do just about everything."
Thirteen percent said budget balancing efforts should focus equally on service cuts and higher taxes, more than doubling that sentiment in previous polls.
When it comes to specifics, people are leery.
By 48 percent to 40 percent, more oppose proposals to gradually raise the eligibility age for Medicare from 65. Only 3 in 10 support slowing the growth of annual Social Security benefits. And more people oppose than favor cutting military spending.
Sentiments about culling savings from Social Security and Medicare were similar among Democrats and Republicans. The strongest opposition to raising the Medicare eligibility age came from people ages 30 to 64. People 50 to 64 were most opposed to slowing the growth of Social Security benefits.
Just over half of Democrats favor cutting defense; two-thirds of Republicans oppose it.
People were about evenly split over an idea voiced by defeated GOP presidential candidate Mitt Romney to put a dollar limit on taxpayers' deductions.
Another idea — ending the tax deduction for home mortgage interest in exchange for lower income tax rates — was favored 42 percent to 33 percent, slightly less support than the proposal received in 2010. Homeowners were closely divided over the proposal.
Just over half the poll respondents say they doubt Obama will be able to reduce budget deficits during his remaining four years in office. In his first days in office in 2009, more people than not thought he would be able to do so.
The poll found little change in the nation's partisan makeup after the contentious presidential election campaign, with 33 percent saying they consider themselves Democrats, 23 percent Republicans and 27 percent independents. That's about the same as in AP-GfK polling over the past six months.
The Associated Press-GfK poll was conducted Nov. 29 to Dec. 3 by GfK Roper Public Affairs & Corporate Communications. It involved landline and cellphone interviews with 1,002 adults nationwide. The survey has a margin of sampling error of plus or minus 3.9 percentage points.
AP news survey specialist Dennis Junius contributed to this report.