WASHINGTON – A new tax on large banks is picking up support in Congress as Democrats target financial institutions that benefited from the Wall Street bailout to help pay for their jobs program and other election-year initiatives.

One senator, Chuck Schumer, D-N.Y., said Tuesday he wants to include the bank tax in a bill stiffening financial regulations, an idea rejected by Banking Committee Chairman Christopher Dodd, D-Conn.

Including the bank tax in the financial regulations bill could make it harder to get Republican support because GOP lawmakers have generally opposed the tax. Republican leaders appeared Tuesday to soften their opposition to the financial overhaul bill, praising bipartisan negotiations that continue to take place. And President Barack Obama telephoned newly elected GOP Sen. Scott Brown of Massachusetts seeking support for the measure.

“I’m convinced now that there is a new element of seriousness attached to this, rather than just trying to score political points,” said Senate Republican Leader Mitch McConnell of Kentucky.

Dodd and the banking committee’s ranking Republican, Sen. Richard Shelby of Alabama, held their second bargaining session of the week Tuesday. They also met to discuss the legislation last week.

“I believe we’re going to get ourselves a bipartisan bill,” Shelby said.

The tax on bank liabilities, which Obama first proposed in January, would raise an estimated $90 billion over the next decade. Democrats say the tax is justified to recoup billions spent bailing out Wall Street.

The White House says money from the tax could be used to reduce the budget deficit, but Democrats in Congress are also looking for revenue to pay for several measures, and some see the financial industry as a politically viable target. Democrats want revenue to pay for a one-year extension of a series of popular tax cuts that expired at the end of 2009, as well as several measures designed to create jobs.

“I think the administration proposal is a common-sense way to make sure the taxpayers are repaid,” Schumer said Tuesday at a Senate Finance Committee hearing on the bank tax.

The House and Senate have both passed bills that would extend about $26 billion in tax cuts that expired at the end of 2009, though the chambers have been unable to agree on how to finance them. The tax breaks include a property tax deduction for people who don’t itemize, lucrative credits that help businesses finance research and development and a sales tax deduction that mainly helps people in the nine states without income taxes.

The banking industry argues the new tax would reduce lending and increase fees for consumers, just as the economy is starting to pick up.

“It’s certainly easy to demagogue the financial services industry right now,” Scott Talbott, senior vice president of government affairs for the Financial Services Roundtable, said in an interview.

Sen. Max Baucus, D-Mont., chairman of the Senate Finance Committee, is planning several hearings to promote the tax.