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The Senate is expected Wednesday to pass its pared-down, $15 billion version of a jobs bill, after five Republicans joined nearly all Democrats in heading off a filibuster Monday.

The broken filibuster left Democrats optimistic that they can attract Republican support for more of their agenda, including health care reform.

“I think this is a good example and a good lead-in to Thursday, and that is there’s a willingness for members to put aside partisan games and to move ahead with what we know is important for the American people and for the growth and the stabilization of our economy,” said White House press secretary Robert Gibbs.

The bill still will need to be squared with a much broader $155 billion version the House passed last year, though House Democratic leaders could pass the Senate bill as is and declare a quick victory.

Democrats in both the House and Senate say this initial bill will be followed by others designed to promote job creation.

In another show of bipartisan cooperation, Senate Majority Leader Harry Reid, Nevada Democrat, and Minority Leader Mitch McConnell, Kentucky Republican, were hammering out details Tuesday morning for another package of measures to extend tax breaks, unemployment benefit payments and government subsidies to help laid-off workers buy health insurance.

A Reid aide could be heard suggesting a one-year extension of unemployment insurance as a McConnell aide jotted down the proposal and Mr. Reid chimed in, pointing to the paper and offering explanations.

The CBO numbers provided a boost to Democrats, who have been on the defensive over the $862 billion Recovery Act.

But the numbers do underscore the administration’s failure to predict the depth of the recession. The White House had predicted peak unemployment of 8 percent without the stimulus, and well less with the stimulus. CBO’s numbers show that peak unemployment could have reached beyond 11 percent without the additional spending.

On Tuesday, House Majority Leader Steny H. Hoyer, Maryland Democrat, said making the 8 percent claim was a mistake.

“Probably shouldn’t have made that claim,” he told reporters. But he said the stimulus act and Congress’ other moves have left the economy in much better shape than before.

He pointed to the Dow Jones Industrial Average, which has gained about 4,000 points since Mr. Obama took office, and said the housing market has stabilized and the number of jobs lost each month has fallen dramatically, though it’s not in positive territory.