The results were similar when people were asked whether they would rather raise the retirement age or cut monthly payments for future generations - 53 percent said they would raise the retirement age, while 35 percent said they would cut monthly payments.
Social Security is being hit by a wave of millions of retiring baby boomers, leaving relatively fewer workers to pay into the system. The trustees who oversee the massive retirement and disability program say Social Security's trust funds will run out of money in 2033. At that point, Social Security will only collect enough tax revenue to pay 75 percent of benefits, unless Congress acts.
Lawmakers from both political parties say there is a good chance Congress will address Social Security in the next year or two - if the White House takes the lead.
In previous polls, Democrats have typically scored better than Republicans on handling Social Security. But the AP-GfK poll shows Americans are closely divided on which presidential candidate they trust to handle the issue.
Forty-seven percent said they trust President Obama to do a better job on Social Security, and 44 percent said they trust his Republican opponent, Mitt Romney. The difference is within the poll's margin of sampling error.
Romney has said he favors gradually increasing the retirement age, but he opposes tax increases to shore up Social Security.
Obama hasn't laid out a detailed plan for addressing Social Security. But during the 2008 campaign, he called for applying the Social Security payroll tax to wages above $250,000. It is now limited to wages below $110,100, a level that increases with inflation. He says any changes to Social Security should be done "without putting at risk current retirees . . . without slashing benefits for future generations, and without subjecting Americans' guaranteed retirement income to the whims of the stock market."
Romney's running mate, Rep. Paul Ryan of Wisconsin, has been a leading proponent in Congress of allowing workers to divert a portion of their Social Security taxes into personal investment accounts.
Romney put Ryan on the ticket Aug. 11. The AP-GfK Poll was conducted Aug. 16-20.
Democrats, Republicans, and independents all favored raising the retirement age over cutting monthly payments. But 65 percent of Democrats and 53 percent of independents supported higher taxes, compared with just 38 percent of Republicans.
The poll involved landline and cellphone interviews with 1,006 adults nationwide. Results for the full sample have a margin of sampling error of 3.9 percentage points.