A useful rule of thumb based on recent occupations is twenty security personnel (troops and police combined) per thousand inhabitants. It's not a perfect figure, but it's useful. One variable factor is the hostility of the population. If I recall correctly the occupation forces in Germany at the end of WWII approached, or even exceded, 50:1000. (In this case I'd actually suggest a higher ratio would be necessary...)
Some figures:
Iran's population in 2003 was roughly 70 million.
In 2003, there were 500 thousand active duty Army troops and 700 thousand National Guard and Army reservists.
Some 70 thousand were deployed in Europe and another 30 thousand in Asia, for a rough total of 100 thousand, and 360 thousand were in needed positions in the US.
Some math:
(70 million/1000) x 20 = 1.4 million
500 thousand + 700 thousand = 1.2 million
1.2 million - 100 thousand - 360 thousand = 740 thousand
Even if the US had been able to call up all the Gaurd and reserve forces, the rule of thumb threshold would not have been reached, even if all it's deployed forces were stripped out of Asia and Europe.
ignoring that figure in Iraq is the main reason we had trouble to begin with.
It would have required at least a pair of Marine Divisions, and probably the 82nd and 101st to pull of a landing at Bandar Abbas (and those troops couldn't land all at once because we don't have enough ships). Most likely 2 MEBs plus a pair of airborne brigades for the initial assault and everything else comes in later. There would not be an invasion via Kuwait as there is no border with Iran and Kuwait. Turkey has a small border with Iran as well, and probably would be just as difficult as in OTL. Invading via Afghanistan is a non-starter because of the logistical issues.
So that leaves a seizure of the port of Bandar Abbas and working from there. Pakistan nor Iraq would likely be sought out as allies for this for various reasons (lots of them).
This would be a full scale war, and would require mobilization, and at least a couple of full sized corps plus the assault corps (so at least 8-10 divisions plus corps and army level assets). This is a big one, and even George W would have to think about this one carefully before going in. He would need something very concrete to get Congress to sign on as well. The only thing I can think of would be Iran attempting to close the Strait of Hormuz and somehow pulling it off.
or actually using a nuke (in which case the US nuclear forces come into play most likely)