This morning, Chuck Schumer went on MSNBC and vowed that Dems would not budge from their position on the payroll tax cut — and would hold the line until House Republicans buckled and agreed to support the Senate compromise extending it by two months.

“Pressure every day is mounting on Republicans,” Schumer said. “All you have to do is let the pressure mount, day in and day out, and they will come back and support the two month. Not a majority of Republicans, but enough Republicans added to the Democrats to pass the bill by a large majority. In a few days, they will fold.”

Which raises a question: Do House Republicans have any leverage at all in this fight at this point?

A senior Senate Republican aide I spoke to this morning said the sentiment among some Senate Republican aides is that the House holds no leverage at all. And he suggested a very interesting endgame in this fight for Dems.

“The House has zero leverage,” this Senate GOP aide says. “If I’m Schumer or Reid, what I’d do is let it expire and force the House to come back the next day and pass it.”

Is it plausible that it could come to this? Could Dems simply allow the payroll tax cut to expire, then hammer House Republicans mercilessly in the press until they come back in January and pass the Senate bill? Dems could continually point out that the Senate has already passed an extension with an overwhelming bipartisan majority, that the President is ready to sign it, and that the only reason the tax cut expired is because House Republicans won’t support the compromise backed by many members of their own party in the upper chamber. And the president has an awfully big megaphone to amplify this message.

A senior Democratic leadership aide said this endgame is a possibility.

“If they refuse to pick it up, it will expire, and we will continue to rake them over the coals in the press,” the Dem aide said. “There are already fractures showing in their facade. At a certain point they are just going to have to cave and cut their losses. Our line is, no negotiations until they pass the Senate compromise. That’s not changing at all.”

The Dem aide stressed that this is not their preferred outcome. “We really don’t want this to expire, but if it comes to that we’ll win the political battle,” he said.

Obviously it remains to be seen whether Dems will hold fast to this strategy, and there are plenty of reasons to assume they might not, given recent events. But this situation does seem unique, in that an overwhelming number of Senate Republicans agree with Obama and Democrats on the temporary extension, and even Senate Republicans don’t see what leverage their House counterparts have at this point, if any.