The poll found 30 percent supported the idea and 15 percent were neutral. Of those opposed to a recalculation, 32 percent said they "strongly opposed" the change, compared with just 11 percent who strongly support it.
Obama rejected a House Republican plan that aims to balance the budget in 10 years with steep cuts in domestic spending.
His remarks reflected the White House's argument that Obama's blend of tax increases and spending cuts have widespread public support and will ultimately change the terms of the fiscal debate in Washington.
"My budget will reduce our deficits not with aimless, reckless spending cuts that hurt students and seniors and middle-class families, but through the balanced approach that the American people prefer, and the investments that a growing economy demands," he said.
Still, Obama has been unable to move House Republicans from their opposition to higher taxes, and his proposed reduction in the growth of benefits drew swift objections from allies.
"The president should drop these misguided cuts in benefits and focus instead on building support in Congress for investing in jobs," AFL-CIO President Richard Trumka said in a statement Friday.
Kansas Gov. Sam Brownback delivered the Republican radio and Internet address, arguing that "the ideas on how to fix the federal government are now percolating in the states."
"You see, you don't change America by changing Washington — you change America by changing the states," he said. "And that's exactly what Republican governors are doing across the country — taking a different approach to grow their states' economies and fix their governments with ideas that work.
Brownback, a former House member and senator, called for a "taxing structure that encourages growth, an education system that produces measurable results, and a renewed focus on the incredible dignity of each and every person, no matter who they are."
AP Director of Polling Jennifer Agiesta contributed to this report.
Follow Jim Kuhnhenn on Twitter: http://twitter.com/jkuhnhenn