On a minor point of Republican bullshit
Neither Putin nor Rouhani is explicitly threatening to deliberately crash the US (and world) economy unless Obama submits to a set of demands. If they were, Obama would no doubt tell them, too, that he refused to negotiate under such duress.
Obama has stated clearly that he is willing to negotiate with the Republicans about whatever issues they want to discuss, but they have to let a clean CR and debt-limit increase pass first -- they have to take the gun away from the hostage's head before real negotiation is possible.
In short, he can negotiate with Putin and Rouhani because they are not making de facto terrorist threats against our country. Right now, the Republicans are.