The vote was 51-49 in favor of the measure but it required 60 votes to pass. The Senate was to vote later Thursday on a Republican proposal to extend the payroll tax cut and pay for it by freezing federal workers' wages for three years and cutting the federal workforce by 200,000.
Senate Majority Whip Dick Durbin, D-Ill., said the GOP approach would "kill jobs" while the Democrats' approach "is to create jobs."
The vote to kill the Democratic plan came after a third Republican senator said a GOP plan could involve raising taxes on high-income people.
"I sense a change in mood -- it's a little more bipartisan," said Sen. Mike Johanns, R-Neb.
"My position has always been, 'Let's not raise taxes,'" he said in remarks quoted by The New York Times. "But on the other hand, I don't want our country to collapse under a mountain of debt. If that means compromise, I am going to do everything to get that done."
His suggestion of raising taxes on the wealthy came a day after Senate Appropriations Committee member Susan Collins, R-Maine, said she supported the "millionaires surtax" but wanted to exempt small businesses from the increase.
Democrats are seeking to reduce the Social Security payroll tax paid by employees by half, to 3.1 percent of wages, a position many Republicans support.
Senate Minority Leader Mitch McConnell, R-Ky., said Tuesday Republicans would not support making up for the lost revenue through a 3.25 percent surtax on annual income over $1 million, which Democrats proposed.
Collins told the Times Wednesday her alternative idea to protect employers from the surcharge would mitigate some Republican opposition.
"What we've been hearing over and over again is that the reason Republicans are opposed to the surtax is because of the concern on its impact on job creation," she said. "Well if you carve out employers you take away that argument."
Senate Finance Committee member Pat Roberts, R-Kan., said Tuesday Republicans had discussed a plan to cover the lost Social Security revenue by approving a small increase in taxes for some high-income people who meet certain criteria. His office did not respond to a United Press International request for further details.
Forty-one senators, including Roberts, and 238 House members signed a "Taxpayer Protection Pledge," promoted by conservative lobbyist Grover Norquist, promising never, under any circumstances, to support a tax increase.
McConnell said Republicans would propose a bill this week to extend the payroll tax cut without the Democrats' surcharge. He wouldn't provide details, but predicted Congress would extend the cut, which expires Dec. 31.
"Let me just put it this way: There will be no Christmas for Congress unless there is an extension of the unemployment insurance benefits," Harkin, chairman of the Senate Health, Education, Labor and Pensions Committee, said at a news conference attended by other House and Senate Democrats, Labor Secretary Hilda Solis and numerous unemployed workers.
"Believe me, we have a number of us on the Senate side. We're not going home. We're not going to have Christmas for Congress until you get an extension of unemployment benefits," Harkin said.
Republican leaders have said they favor an extension as long as the cost is offset by cuts elsewhere. But lawmakers have not found a bipartisan solution to accomplish that, Roll Call reported.
Harkin could keep the Democratic-controlled Senate in Washington by demanding a vote on adjournment, rather than allowing the usual unanimous consent without a vote. His demand would require a majority vote to get the senators out of the Capitol.
Celebrity Families of 2014 [PHOTOS]