The House, however, is expected to vote on the bill again as early as Wednesday.
Without an extension, payments would continue to phase out for more than 200,000 people a week. The last extension expired at the end of May. House Democrats said more than 1 million people have already lost benefits.
Congressional Democrats have been trying for weeks to pass the extension as part of a larger tax and spending package, but the larger bill stalled in the Senate. On Tuesday, House Democrats brought up a standalone bill on unemployment benefits.
Democrats brought up the bill under a special procedure in which no amendments were allowed and debate was limited. Under the procedure, the bill needed a two-thirds majority to pass. The vote was 261-155, short of the two-thirds needed.
House Democrats now plan to bring up the bill again under regular business, in which the bill would need only a simple majority to pass, said Rep. Sander Levin, D-Mich., chairman of the House Ways and Means Committee.
Levin said he expects the House to vote on the bill again Wednesday. In Tuesday's vote, nearly all Democrats voted in favor of the bill, while most Republicans opposed it.
"America's unemployed workers cannot wait any longer for us to do the right thing," said Rep. Jim McDermott, D-Wash., chairman of the House Ways and Means subcommittee on income security.
The measure would provide up to 99 weekly unemployment checks averaging $335 to people whose 26 weeks of state-paid benefits have run out. The benefits would have been available through the end of November, at a cost of $33.9 billion. There were no offsets in the bill, so the cost would have added to the budget deficit.
"The American people know it isn't right to simply add the cost of this spending to our already overdrawn national credit card," said Rep. Dave Camp of Michigan, the top Republican on the Ways and Means Committee. "They want to help those in need but also know that someone has to pay when government spends money."
Republicans accused Democrats of playing politics with the measure, since they could have brought up the bill Tuesday in regular order and passed it with a simple majority.
It's a tough vote for some lawmakers who want to help constituents hit hard by the recession but are wary of being labeled big spenders. The economy is starting to pick up, but unemployment is still high as the nation continues to struggle from the loss of more than 8 million jobs. At the same time, angst over deficit spending is growing as midterm congressional elections near in November.
"We are a community of people. When people lose their jobs and can't find them, we don't stand and simply stand idly by," Levin said.
Rep. Kevin Brady, R-Texas, said, "People are frightened by the amount of debt this country owes."