House Speaker Nancy Pelosi, D-Calif., said Thursday that getting President Bush and congressional Republicans to agree on the need for a second stimulus package is vital for moving legislation to help boost the nation’s economy.

“This has to be bipartisan. We have to have a signature,” Pelosi said.

Senate Appropriations Chairman Robert C. Byrd, D-W.Va., kicked off the second round of the stimulus debate Wednesday, unveiling a summary of a proposal that totals $24 billion.

Pelosi said that a second stimulus package would need to adhere to the same criteria Democrats sought for the first measure earlier this year: that it be “temporary, targeted and timely” and “create jobs, grow the economy and provide for disaster assistance.”

“Much of what Sen. Byrd has fulfills that bill,” Pelosi said.

The Speaker earlier had vowed to enact a second measure, totaling at least $50 billion, before Congress leaves this year. But the president and congressional Republicans have been less enthusiastic about the idea, repeatedly arguing that lawmakers should wait to assess the impact of the tax rebates and other incentives enacted in February.

House Minority Leader John A. Boehner, R-Ohio, said that he doubted a second package is needed, and added that if one is negotiated he wants to see something similar to the first bill’s tax rebates.

“I have serious doubts about whether we really need a second stimulus, and I have greater doubts about what it will look like under a Democrat Congress,” he said. “It will just be a giveaway that will be well-meaning, well-intentioned but a big waste of taxpayers’ dollars.”

The first stimulus “worked and is working,’’ Boehner said.

Pelosi also touted the benefits of the first package. The economy grew 1.9 percent in the second quarter of 2008, strongly aided by the legislation, she said.

Bush has yet to express any support for a second stimulus, saying he wants to see the impact of the first one.