So here’s the next move in the payroll tax cut fight: Senate Dems will force Republicans to vote again on an extension, and, notably, they will again insist that it be funded by a small surtax on millionaires, albeit a an even tinier one than last time.

The new offer is a variation of the last Dem proposal, which Republicans blocked last week in the Senate.

The new proposal, a Senate Dem aide says, drops the rate of the millionaire surtax to just under 2 percent on income over $1 million (before it was at 3.25 percent). But it contains other measures to pay for the extension designed to attract GOP support.

For instance, the extension would be funded by some small revenue generators that both sides agreed to during the deficit supercommittee talks. It also includes means testing of unemployment insurance and food stamps for earners over $1 million.

“We think it will be hard for Republicans who do not want to oppose a tax cut for the middle class to vote against this plan,” the Dem aide says. Of course, as Brian Beutler reports, GOP leadership aides are saying that even a smaller surtax on millionaires are a nonstarter.

But the Dem game plan here is to go around the leadership by increasing pressure on moderate Republicans who, in the end, want to support a payroll tax cut extension. The idea is that when Republicans rejected their own proposal last week — which would have been paid for by spending cuts — they revealed that many in the Senate GOP caucus are opposed to extending the payroll tax cut no matter how it’s paid for, not simply because it’s funded by a millionaire surtax.

Previously, Republicans could explain their opposition to the Dem plan by saying Republicans have their own proposal. Now that the GOP proposal can’t even get support from many Republicans, Dems are hoping that moderate Republicans will feel more pressure to support a Dem-proposed compromise.

Hence the new Dem proposal, which shrinks the surtax on millionaires even further. In theory, that should make the proposal harder for self-described moderate Republicans to reject. But presuming they do, the Dem proposal will again spotlight just how adamant GOP opposition to any tax hikes on the rich remains.

UPDATE: Obama, speaking to the press right now, again pressured Republicans to pay for the extension, and mocked the idea among some GOPers that this tax cut — unlike the extension of the tax cuts on the rich — have to be paid for:

“Some Republicans who have pushed back against the idea of extending this payroll tax cut have said, `We’ve gotta pay for these tax cuts.’ I’d just point out that they haven’t always felt that way. Over the last decade, they didn’t feel the need to pay for massive tax cuts for the wealthiest Americans, which is one of the reasons we have faced such large deficits...

“This isn’t just a political fight. Independent economists, some of whom have in the past worked for Republicans, agree that if we don’t extend the payroll tax cut, and we don’t extend unemployment insurance, it will hurt our economy...It’ll take money out of the pockets of Americans just at the time when they need it... My message to Congress is this: Keep your word to the American people, and don’t raise taxes on them right now.”