The package of tax cuts and new spending was blocked Tuesday night by the chamber's Republican minority 50 to 49, 10 votes short of the 60 it needed to advance in the full 100-member Senate.
Senate Majority Leader Harry Reid-D-Nev., switched to no from yes in a technical move that will let him bring up the measure again.
One Republican, Sen. Tom Coburn of Oklahoma did not vote.
Obama criticized Republicans afterward for rejecting initiatives they previously supported.
The vote "is by no means the end of this fight," he said in a statement.
The administration "will now work with Sen. Reid to make sure that the individual proposals in this jobs bill" -- including payroll tax cuts, unemployment benefits and construction spending -- "get a vote as soon as possible," he said.
"It's time for Congress to meet their responsibility, put their party politics aside and take action on jobs right now," he said.
Votes on the bill's pieces could begin as early as next week, Senate Democratic aides told The New York Times.
House Majority Leader Eric Cantor, R-Va., said before the vote Republicans would support legislation that could promote hiring and economic growth.
Obama's bill calls for $175 billion in new spending on highways and other public works, an extension of unemployment benefits and aid to states to prevent teacher layoffs. The bill would provide $272 billion in tax relief for individuals and businesses.
It includes a proposed 5.6 percent surtax, starting in 2013, on personal income above $1 million. Fewer than 350,000 tax returns this year showed income of more than $1 million, the Congressional Joint Committee on Taxation said.
Democrats said Republican opposition to the bill was based solely on a desire to see Obama fail.
"I guess Republicans think that if the economy improves, it might help President Obama," Reid said. "So they root for the economy to fail and oppose every effort to improve it."
McConnell said Republicans saw the situation totally the opposite.
"Democrats have designed this bill to fail -- they've designed their own bill to fail -- in the hope that anyone who votes against it will look bad," he said. "This whole exercise is a charade that's meant to give Democrats a political edge in an election that's 13 months away."
Fourteen million Americans are unemployed and the unemployment rate has been 9.1 percent for the past three months.
In November 2008, when Obama was elected, it stood at 6.8 percent. In January 2009, when he took office, it was 7.8 percent. It peaked at 10.1 percent in October 2009.
Celebrity Families of 2014 [PHOTOS]