Obama will have to swallow spending cuts on and some restructuring of entitlements anyway; he will be in hot water with his base for accepting those, and he has, according to his public statements, expressed willingness to take that hit. The reason the Boehner deal is better than the Reid one for Obama is that the former has revenue enhancements, the latter doesn't. If Obama takes the Boehner deal, he can at least say he got them, which will at least play some with the Dems and even independents, who favor by around 60%, some revenue enhancements. If he takes Reid, he gets no revenue enhancements just in trade for not being hit with the debt-ceiling threat again; there's not nearly as much upside, nobody will give him much credit for that.
Do you think there's any meat to the Obama administration's argument that a short debt ceiling extension would cause economic instability and bond problems? To me those claims sound strike me as an half-assed explanation to avoid the electoral problems a Boehner deal might entail. I don't think the President has any other option but to take the deal, Boehner's rhetoric is pretty strong and would win popular support if Obama doesn't take it and we get close to the deadline.