In private meetings and publicly reported comments, Republican leaders have been working to back away from the $4 trillion deal that President Obama and Speaker John A. Boehner floated last week, and return the focus to a variant of the $2 trillion deal that the Biden negotiators were closing in on three weeks ago. But the deal they want — and that they’re considering acting on unilaterally — is a deal that Democrats say is not and was not on the table: It’s the spending cuts the negotiators agreed to without the revenues that led House Majority Leader Eric Cantor to abandon the talks.

A source passed along the slides from the presentation that Cantor is using to sell the deal to his caucus. The slides provide more detail than we’ve yet seen on the specific cuts that Cantor, at least, believes were agreed to in the Biden talks. It calls those cuts “Obama’s version: the Biden framework,” which Cantor says was revenue neutral, and then compares them with “Reid’s deal,” a trillion-dollar package that avoids entitlement cuts altogether, and “Obama’s version: The Big Deal,” which is the $4 trillion deal that fell apart last weekend.

The final slide lists the GOP’s “Agreement Principles”: No tax increases, which rules out “the big deal”; a dollar-for-dollar match between the increase in the debt ceiling and the spending cuts, which rules out “Reid’s deal,” unless the White House agrees to a short-term increase in the debt ceiling; and spending controls and caps, which aren’t included in any of the deals. Here are the slides:

Democrats reject the idea that the “Biden framework” actually exists. The talks, they say, have operated under the rule that “nothing is agreed to unless everything is agreed to,” and since the talks broke up before there was agreement on revenues or fiscal controls, the spending cuts were not, in fact, agreed to. There is no Biden framework.

Republicans, I’m told, plan to argue that the Democrats did agree to these spending cuts as part of a final deal, and since they’ve already made clear that they believe they could support these cuts, it makes no sense to let the debt ceiling collapse just because the two sides can’t agree on taxes. To that end, House Republicans are likely to move a bill next week that includes these cuts, perhaps without some of the Medicare savings, and also raises the debt ceiling. Then, if Senate Democrats and the White House refuse to pass the legislation, they figure that they can blame the Democrats for letting the debt ceiling collapse, as Republicans will have already passed legislation that could have lifted it.

In theory, President Obama rejected such a strategy in Monday’s press conference. “If the basic proposition is ‘it’s my way or the highway,’” he said, “then we’re probably not going to get something done because we’ve got divided government.” But Republicans know the White House is terrified of what default could do to an already fragile recovery. Given the choice between their way and a fresh recession, they think there’s some chance he may change his mind.