I'm not sure if the administration is spinning Politico here, or if they really believe Republicans will have to embrace a budget deal:

White House officials maintain that some kind of deal is achievable, if for no other reason than Republicans, who have attacked Obama for punting on the issue, will be forced to negotiate in good faith or lose credibility.
“They are in a box,” said an Obama ally.
“The president is optimistic we can get something done,” Gene Sperling, chairman of the National Economic Council, told POLITICO.
The sense in the West Wing is that cooler heads in the Senate – eager to forge some kind of deal to attack the country’s debt ahead of next year’s elections – will agree to some kind of revenue enhancements, forcing House Republicans to follow suit.

What? I see the administration listing two dynamics that supposedly will force House Republicans to embrace a deficit compromise. The first is that, having attacked Obama on the deficit, they'll "lose credibility" if they don't meet him halfway. I don't even know what to say about this. Their theory is, what, the threat of a mildly disapproving column by David Brooks will force House Republicans to violate the central tenet of their partisan and ideological creed?

And then the belief that Senate Republicans will jump first on a deal, which in turn will pressure House Republicans to follow suit. This seems even more delusional than the other scenario. The Obama era is filled with examples of Senate Republicans negotiating on bills behind closed doors, and then pulling back when party leaders and/or interest groups apply pressure. It seems far more likely that the lack of action by House Republicans will cause Senate Republicans to back off. Why walk the plank on the party's central issue, and and run the very high risk of facing and losing a primary challenge, when it might just die in the House?

And even if Senate Republicans do go first, how does this "force" House Republicans to follow suit? They can just attack the tax hikes. What pressure is going to force them to act? The fear of being seen as more ideologically pure than some apostate Senate Republicans? I don't understand what recent experience or even theoretical scenario could cause House Republicans to see this as a dire threat.

I can believe that Obama feels the need to project earnest interest in a bipartisan deal, so he can say he tried. Perhaps this strategy is causing the administration and its allies to spin out fanciful scenarios whereby this works, because admitting it's highly implausible undermines their claim to have tried. But do they actually believe this?