Perhaps the administration's best argument for the deal that is being floated is that John Boehner is too budgetarily-illiterate and politically inept to actually press any advantage on the debt ceiling.
The White House laughs off the GOP’s theory that they can use the debt ceiling to extract big spending cuts without any further tax increases. For one thing, Boehner wouldn’t know how to achieve his “dollar-for-dollar” rule if you gave him total control of the budget. Raising the debt ceiling will cost around $1.5 trillion through 2014. Boehner has never named spending cuts even in the neighborhood of $1.5 trillion. In fact, he’s never named many entitlement cuts at all. Republicans actually seem terrified of entitlement cuts.
Indeed, the Republicans are playing with fire if they threaten to default the country again, but that is triply true when you realize that they can't even craft a bill that would do what they say that they want to do and they are terrified of even trying to craft such a bill.
Goal number one (before the cliff) has always been to break the grip of the Norquist pledge, while the next most important goals were to help the economy by extending unemployment insurance and stimulative tax credits, and to (ideally) end the fuss about the debt ceiling. In the floated deal, most of this is accomplished. Although the debt ceiling remains a problem, the quoted bit above explains why they are not worried about it. Plus, there are (so far) no cuts beyond those included in the sequester. If they want money for the Pentagon, we can trade it for money for Head Start. This is the downside of not reaching a Grand Bargain. We will have to barter for everything we value in the federal budget, which means we can't be fully focused on immigration reform or assault weapons or addressing climate change.
The floated deal provides a LOT that we would not otherwise get, yet I am still not sure that the White House expects it to pass, and a big part of Obama's appearance this afternoon was about making the Republicans look especially bad and petty if they do not agree to a deal. Basically, the president said that a deal was almost done and that there were only minor, insignificant things left to resolve. He taunted Congress, calling them totally ineffectual and openly laughing at them. This led, inevitably, to a bunch of butt-hurt tweets from Republicans and Republican aides about how Obama was "moving the goalposts" and trying to "sabotage a deal." Yes, getting them to write those tweets was part of the plan to maximize how bad the GOP will look if they don't agree to a deal.
In other words, the president promised more than had been agreed to and dared the Republicans to blow up the talks. He can live with the deal he outlined, but he can live without it, too.