Education and Labor Chairman George Miller (D-Calif.) said this morning that he would still like to see a vote on middle-class tax cuts before the House adjourns Thursday.

“I happen to believe that that’s a vote that should take place,” he said on CNBC. “I think we should support a tax cut for those families up to $250,000. I think that would be an important signal, but we’ll just have to see where the votes are.”

Miller is a close confidante of Speaker Nancy Pelosi (D-Calif.), who has been pushing behind the scenes for a vote for several weeks but has run into resistance from Majority Leader Steny Hoyer (D-Md.). Hoyer has questioned the value of holding a vote with the Senate having already decided to punt until after the elections. A sizable group of moderates wants to vote to extend all of the Bush-era tax breaks or punt the issue until after the elections, not vote on a single piece of the tax package.

Democratic leaders are expected to discuss the issue later Tuesday. If a vote is held, it would likely be on the suspension calendar to prevent Republican amendments. That requires a two-thirds majority to pass, giving Republicans the power to defeat the bill on the floor.

A suspension vote would present the GOP with a difficult choice: vote to defeat a tax cut for the middle class or hand Pelosi a victory heading into the elections. Likewise, moderate Democrats, many of whom have demanded an extension of all of the tax cuts, would be placed in an awkward spot as well.

Leadership has discussed allowing a second suspension bill that would extend the tax breaks for some higher income Americans — but they would be placed in an awkward position politically if that second bill gets majority support but fails to get a two-thirds majority. Republicans would be sure to accuse leadership of using House procedures to block the will of the House. And GOP leaders have already warned that Democrats should not count on their votes unless there is a full and fair debate, and a suspension bill with no amendments isn’t what they had in mind.

Miller acknowledged that some want tax cuts for income levels above $250,000 but that there is a serious question about whether cuts for the wealthy are affordable and necessary.

“If that’s the price of getting the cuts for middle-class wage earners, then I think that’s a problem,” Miller said.

If no vote takes place before the elections, Miller said the issue should be dealt with in a lame-duck session rather than kicked into next year. It wouldn’t be good for the economy to wait, he said.