If Wishes Were Ponies...
... then Oliver Willis and Nick Beaudrot would be right that "[m]ilitary strikes against against Iran would quite clearly be an act of war; without Congressional authorization it would pribma facie be an impeachable offense." In the real world, though, I didn't see Bill Clinton getting impeached for bombing Serbia without congressional authorization even by a congress that was eager to impeach Bill Clinton so I wouldn't get my hopes up on that one.
Congress' de facto war powers have been reduced to the need to get congressional approval for war-related spending. What we just saw with Iraq, though, is that according to the media, if Democrats vote for a funded withdrawal of troops, and then Bush vetoes those funds and demands that Democrats give him a blank check, then it would be a failure to "support the troops" for Democrats to refuse to cave to this demand. We've also seen that many -- if not most -- congressional Democrats accept this framing. So if Bush decides he wants to bomb Iran, nobody in congress is going to stop him. Dana Priest, though, speaks for surprisingly many journalist when she says:
Frankly, I think the military would revolt and there would be no pilots to fly those missions. This is a little bit of hyperbole, but not much. Just look at what Gen. Casey, the Army chief, said yesterday. That the tempo of operations in Iraq would make it very hard for the military to respond to a major crisis elsewhere. Beside, it's not the "war" or "bombing" part that's difficult; it's the morning after and all the days after that. Haven't we learned that (again) from Iraq?
To me, though, it's important to avoid overstating the degree of military opposition to a bomb Iran policy. As best I can tell, the Army is dead-set against it. But the Army wouldn't be carrying the mission out anyway. It'd be shocking for the Air Force to suddenly come to appreciate the strategic limits of air power. In their minds, bombing Iran won't compound the error of Iraq; rather, it'll show the manifest benefits of doing things their way rather than getting bogged-down into an Army-style quagmire.