This time, the bill was narrowed to provide $35 billion to state and local governments to prevent layoffs of teachers, police officers and firefighters. To offset the cost, the bill would impose a surtax of 0.5 percent, starting in 2013, on income in excess of $1 million.
Despite the vote Thursday, Democrats said they hoped to gain a political edge, by forcing Republicans to vote on this and other discrete parts of broader legislation proposed by Mr. Obama to create jobs and revive the economy.
Campaigning for his $447 billion jobs package this week in North Carolina and Virginia, Mr. Obama suggested that Republicans could not understand the whole thing all at once, so he said “we’re going to chop it up into some bite-sized pieces.”
The Senate last week blocked consideration of the larger bill, which included a 5.6 percent surtax on income over $1 million.
Republicans objected to the tax and said the bill would be no more successful than the economic stimulus law Mr. Obama signed in February 2009.
The vote late Thursday generally followed party lines. Two Democrats — Senators Ben Nelson of Nebraska and Mark Pryor of Arkansas — and Senator Joseph I. Lieberman, independent of Connecticut, joined Republicans in voting against immediate consideration of the bill for public employees.
Both parties seized on the smaller bill to draw contrasts in advance of the 2012 elections.
Democrats said the bill would save or create jobs for nearly 400,000 teachers and force millionaires to make a small sacrifice for the benefit of the nation.
“The massive layoffs we have had in America today are rooted in the last administration,” said the Senate majority leader, Harry Reid, Democrat of Nevada. “It is very clear that private sector jobs have been doing fine. It is the public sector jobs where we have lost huge numbers.”
The Senate Republican leader, Mitch McConnell of Kentucky, derided the Democrats’ proposal as “a government jobs bill.” He said it would “impose a permanent tax hike on about 300,000 U.S. business owners and then use the money to bail out cities and states that cannot pay their bills.”
The bill would pay for the hiring, rehiring and retention of school employees, law enforcement officers, firefighters and other emergency workers.
Public employees and labor union leaders joined Democrats, including Vice President Joseph R. Biden Jr., at a rally on Wednesday urging the Senate to pass the bill. Mr. Biden said that because of police layoffs, “murder rates are up, robberies are up, rapes are up” in many cities.
Democrats see an urgent need to aid state and local governments, whose revenues have not fully recovered from the recession. The Congressional Budget Office said that less than one-third of new spending under the bill would occur in the coming year, however. It foresees annual spending of roughly $11 billion in 2012 and 2013, followed by $7 billion in 2014, $5 billion in 2015 and $1 billion in 2016.
Unable to pass the full bill devised by the White House, Senate Democrats hope some of the individual pieces will prove more popular with Republicans. Other smaller bills to be taken up in turn would expand the current payroll tax cut for employees, increase spending on transportation and public works projects, and provide incentives for the hiring of unemployed veterans.
For their part, Senate Republicans pushed Thursday for a bill that would repeal a tax compliance requirement that businesses consider extremely burdensome. The provision, adopted in 2006, requires federal, state and local government agencies to deduct and withhold 3 percent of payments they make to many suppliers of goods and services. The requirement was adopted after federal auditors found that thousands of government contractors had substantial amounts of unpaid federal taxes.
Democrats supported the intent of the bill, but blocked its consideration because it would also require unspecified cuts in spending for domestic programs.
Senator Scott P. Brown, Republican of Massachusetts, said, “We need to repeal once and for all this onerous and costly unfunded mandate.”
WASHINGTON — For the second time in 10 days, the Senate on Thursday rejected Democratic efforts to take up a jobs bill championed by President Obama.
Republicans described their proposal as a jobs bill because, as Mr. Brown said, it would “repeal a part of our tax code that promises to kill jobs.”
Enforcement of the requirement has been delayed several times. As part of his jobs bill, Mr. Obama proposed a further delay, to 2014. Businesses say the withholding will disrupt their cash flow and cause administrative headaches.