I think those Gang of X negotiations can only really work with the tacit endorsement of the parties.
Leading up to the fiscal cliff, IIRC, Boehner basically gave the Senate GOP a green light to reach their own deal, with the expectation that it would get a floor vote in the House (which he badgered his caucus into accepting).
If the House GOP leadership doesn't pass the responsibility for negotiating to the Senate, then the idea of cutting a side-deal gets way messier, for the same reason you pointed out it would be good for Obama. Without an understanding in place that any negotiated solution would get seriously considered, the end result would just be a dead-end bill that only served as a political cudgel for Obama to use against Boehner. Pretty much everyone involved (and excluded for that matter) would understand this. Boehner would flip out on Mitch McConnell, who would let the rest of the caucus know the deal.
It's not strictly impossible that it could happen. But you'd need at least five GOP Senators willing to break ranks in a very disruptive way, because of strong personal feelings about some aspect of the policy involved, or whatever. I'm really, really, really skeptical that would happen in general, and also in particular with McCain (who seems to still hate
That One) and Graham (who's got a South Carolina primary coming in a year and a half).
