There are a lot of assumptions in a scenario like that. The biggest assumption is that our military and the Israeli commanders (civil and military) could get so out of synch that such a loggerhead could come to pass. The second is that it would all play out so fast that there would be no time for a before hand warning of consequences and establishment of sufficiently robust back channel communications between the U.S. Iran.

Then there are the missing bits of scenario information to consider. What and how was attacked? What is the Iranian response? A simple bombing of a reputed nuclear site that actually does little real damage with minor Iranian response might just be ignorable by Obama. Were there enough warning signs and strain between Israel and Obama might cause Obama to open a secret channel to Iran, through which they would then play act some pretend sparring back and forth. Then the real consequences to Israel from Obama would happen over time after the election.

But given your assumptions and minimal scenario I would go with the Pentagon. Of course, that's my desired outcome, so I'm biased.

As long as we are playing scenarios, I'll throw out mine. What if the whole thing is a setup by the U.S. military to unseat the current Israeli extremist leadership?

Hmmmm. How where did I put that stuff I was smoking.