"We shouldn't force his hand, we should let the Republicans dangle out there with their divisions exposed and keep hammering them on holding middle class tax cuts hostage for $700 billion in debt-financed tax cuts for the wealthiest 2 percent of Americans," the aide said.
A White House official told TPM earlier today they will keep after Boehner on the issue, but they are deferring to Speaker Nancy Pelosi as to whether she'll hold floor debate on a vote.
After a separate conversation with a Democratic leadership aide, it's sounding like a vote isn't even a remote possibility, especially if the Senate tries to take action first.
"You don't need a vote in the House to say the party is blocking tax relief for the middle class - you can just point and say, 'Look! Senate Republicans blocked it,'" the aide said. "If Republicans killed a tax cut, that could be potentially game changing for Democrats in both chambers."
Democrats think Boehner is now squeezed by conservatives in his caucus unwilling to compromise with Obama.
"We didn't expect yesterday he would give us that gift, but he did," the aide said. Now, the party sees itself as having a "healthy debate with Republicans on what to do on tax policy," and helping further the goal of making November a "choice" election instead of a referendum on the crappy economy.
"It looks as though Republicans are standing in the way of a tax cut for the middle class to take care of the super rich," the aide said.
(Greg Sargent has a counter-argument that it doesn't help the Dems.)
Nothing is for certain. Remember this spring, when Democrats promised to hold a vote on Rep. Paul Ryan's Social Security and Medicare slashing budget? Yeah, that never happened.
Party aides now tell me that's not likely, for the same reason there won't be a tax cuts vote. They say it's better to use it politically in the few weeks they have left to convince voters they deserve to keep Congressional control.
Whopper of a late update: Another senior leadership aide called TPM about an hour after this post was published to say that leadership is still considering all of its options, including a vote after all. In remarks that highlight disagreement within the Democratic caucus, the aide said leadership is "still in discussions" and that many top Democrats want to force a vote.
"We may have a vote anyway to get people on the record," the aide said. "There are a number of leaders who would like a vote even if the Senate is not able to get to 60 votes. It's good for us, it shows we're for the middle class, they are for the rich."