House Speaker Nancy Pelosi should bring up for a vote President Obama's tax-cut deal with Republicans, an influential House Democrat said Thursday.

Rep. Barney Frank (Mass.) — the top Democrat on the Financial Services Committee — said that Pelosi (D-Calif.) should present lawmakers with the chance to vote on the president's plan and an alternative proposal during the lame-duck session.

"In the end I think she’s obligated to allow a vote on the president’s plan, but also on an alternative," he said during an interview on Bloomberg Television. "I think she should see if we can make changes. But I do think the president's plans should be voted on as well."

Pressure from Frank comes after his colleagues on Thursday took a symbolic vote against the Obama plan, which would renew all the Bush tax cuts for two years in exchange for a 13-month extension of unemployment benefits. 

The outgoing Speaker said after the vote that she will continue discussions with the White House to try to alter the deal, even though Vice President Biden said Wednesday the terms are non-negotiable. 

Some congressional Democrats are wary that extending negotiations on the deal could push other issues to the side, like a stalled nuclear-arms treaty with Russia and a repeal of the military's ban on openly gay service members.

Frank reiterated he will likely vote against the compromise if it comes up for a vote. He said that he wants to see changes made to the estate tax provisions. The tax will rise from zero to 35 percent on estates valued over $5 million next year.

"They are going to be making some changes. I would see if we can get the votes to make some changes, especially in the estate tax," he said. "A handful of people are going to be benefited, people who are so wealthy that they don’t even know there’s a benefit."