"It has to be done," she said of raising the borrowing limit. "We shouldn't risk our reputation or spend money and time arguing about it. We have to pay our debts."
The survey showed slight shifts in concerns about the economy and federal budget deficits. Eighty-six percent consider the economy a top issue, down 5 percentage points from last summer, while 76 percent have the same view on federal deficits, up 7 points since then.
Around one-third expect the economy to worsen over the next year, the highest figure in AP-GfK polling in nearly two years. Less than 1 in 4 think the economy is in good shape, a fairly stable number since last summer.
Despite the slight edge people give the GOP's debt limit path, the survey showed Obama with some advantages as he begins his second term.
Fifty-four percent approve of how he is handling his job, a figure that has changed little over the past year. That is more than triple Congress' 17 percent approval rating, which edged down 6 percentage points since early December, before the two sides' "fiscal cliff" fight ended with Republicans largely accepting Obama's demands to raise taxes on the country's highest earners.
Democrats also have a slight 41 percent to 36 percent advantage over Republicans as the party more trusted to handle the economy.
Both Obama and Congress have fallen in the public's esteem after their last battle over the debt ceiling.
In AP-GfK polling in June 2011, the president held a 52 percent approval rating. By August, it had declined to 46 percent after down-to-the-wire negotiations with Congress. Congressional approval ratings fell even further, from an already weak 21 percent in June to just 12 percent after the year's debt limit standoff finally ended.
When it comes to finding savings to balance the budget, nearly half prefer cutting government services as the GOP wants, 3 in 10 would rather increase taxes and about 1 in 10 would do both. The percentage backing cuts in federal services has dropped 13 percentage points since the spring of 2011, while the number supporting tax cuts has changed little.
The poll also highlighted how public support dwindles when people are asked about specific cuts.
Given four ideas for reducing budget deficits, only one got majority support: charging top earners higher Medicare premiums, backed by 60 percent. That included roughly even proportions of Democrats and Republicans, and majorities of all income groups in the poll.
Only 30 percent back slowing the growth of annual Social Security benefit increases, which Obama agreed to accept in failed talks with Boehner on crafting a deficit-reduction compromise during the "fiscal cliff" fight. Just 35 percent support gradually raising the current Medicare eligibility age of 65, and 41 percent support defense cuts.
The poll involved landline and cellphone interviews with 1,004 randomly chosen adults and had a margin of sampling error of plus or minus 4 percentage points. It was conducted from Jan. 10 to 14 by GfK Roper Public Affairs and Corporate Communications.
AP news survey specialist Dennis Junius contributed to this report.