The Iranian people won't fight to save the regime.
The regular army won't fight to save the regime.
The rich mullahs in gov't will flee.
The regime will begin to crumble as soon as they realize that the U.S. means business and is coming in after them.
The political reality is, while we wait, people are being killed and the American public is getting fed up. The public will force the President to leave Iraq. That's the reality of waiting.
I think you're wrong about not being able to make a sufficient case to the American people. The Iranian regime has threatened us sufficiently enough to make the case that their threats are an act war against us.
As for who supports whom, I spoke to this Iranian just last week, and he maintains that while the cities are anti-government (esp. the students), the countryside is overwhelmingly pro-Mullah.