“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.