"I think people realize that was a temporary thing," said Sen. Mark Begich, D-Alaska.
Rep. Richard Neal of Massachusetts, a senior Democrat on the Ways and Means Committee, said he thinks there is evidence that the tax cut helped the economy. But, he added, "I'm not sure that it met expectations."
House Democratic leader Nancy Pelosi of California said she, too, wants to let the tax cut expire.
Larry Summers, Obama's former economic adviser, is a lonely voice in Washington calling to extend the payroll tax cut. He said in a recent speech that the economy is too fragile to reduce workers' incomes.
Obama pushed for the tax cut in late 2010 as a way to increase workers' take-home pay to help boost consumer spending and provide a spark for the economy. Economists were divided on the economic benefits. Many said it probably helped increase consumer spending but there was no consensus on the magnitude.
The initial tax cut was for only a year, and many Republicans in Congress wanted to let it lapse at the end of 2011. But Obama and Democratic lawmakers successfully fought to extend it through 2012.
Obama, however, didn't include the tax cut in his 2013 budget proposal, and Treasury Secretary Timothy Geithner told Congress this year that he saw no reason to extend it again.
White House spokeswoman Amy Brundage wouldn't rule out an extension but wouldn't commit to one, either.
"The president fought extremely hard last year in the face of Republican opposition to ensure that the payroll tax cut was extended," Brundage said. "There are a number of tax issues that Congress will have to deal with at the end of the year, this being one of them, and we will continue to evaluate all of the options available to us at that time."
Romney's campaign hammers Obama almost every day for proposing to let Bush-era tax cuts expire for individuals making more than $200,000 and married couples making more than $250,000. But Romney's tax plan would let the payroll tax cut expire, an issue he doesn't mention on the stump.
Romney's campaign declined to discuss the issue.
Follow Stephen Ohlemacher on Twitter: http://twitter.com/stephenatap