The Republican measure, which would have paid for a one-year tax-cut extension by freezing federal workers' pay and cutting so-called discretionary spending, fell 20-78 Thursday night.
Senate Minority Leader Mitch McConnell, R-Ky., said Tuesday most Senate Republicans favored extending the payroll-tax cut.
Senate Majority Leader Harry Reid, D-Nev., capitalized on what Democrats called an embarrassment for McConnell.
"Republicans spent this week trying to convince us that they support middle-class tax cuts, but ... a majority of Senate Republicans voted against their own bill, calling into question whether they support middle-class tax cuts at all," he said.
Sen. Jerry Moran, R-Kan., said he opposed extending the tax cut because it would cost the country money.
"When are we going to admit that we are broke?" he said. "We are putting off difficult decisions and leaving it up to our children and grandchildren to pay for our irresponsibility."
The fall of the GOP bill followed the fall of a Democratic version of the same bill.
The Democratic version won a 51-49 majority, nine votes short of the 60 needed for passage. That bill would have funded the 50 percent reduction in the Social Security payroll tax paid by employees with a surtax on people earning more than $1 million a year.
Leaders of both parties insisted an agreement to extend the tax holiday was likely before it expires Dec. 31. If an agreement is not reached, virtually all wage earners would be hit with a tax increase Jan. 1.
House Speaker John Boehner, R-Ohio, said ahead of Friday morning's meeting that despite the defeat of both bills in the Senate, "I do believe there's enough common ground between where the White House and Democrats are and where Republicans are for us to move this legislation and to do so quickly."
President Barack Obama called the Senate rejection of the Democratic version of the bill -- which Democrats say would save the average U.S. family $2,500 next year -- "unacceptable."
"It makes absolutely no sense to raise taxes on the middle class at a time when so many are still trying to get back on their feet," he said.
Workers this year have seen their payroll taxes cut to 4.2 percent of their wages from 6.2 percent, saving an average family $1,000. Democrats wanted to cut that further to 3.1 percent, adding another $1,500 in savings, and extend the tax break to employers.
They would pay for the extension with a 3.25 percent surtax on income above $1 million.
Republicans said their plan would be funded by freezing the pay of federal workers and cutting the government workforce by 10 percent through attrition, while cutting discretionary spending.
The payroll-tax cut is only one issue Congress must tackle by Dec. 31.
Lawmakers also face pressure to extend unemployment benefits another 99 weeks and adjust doctors' Medicare payments so physicians don't see an abrupt decline in their fees.
Congress also must act by Dec. 16 to continue funding the government.