Too sanguine. Hussein invades Jordan to 'save' it from 'an Israeli-backed US coup'. Because we have only a few thousand troops in country they are rolled up; at least until Israeli forces intervene, which they surely will.
This leaves Hussein with partial control of Jordan, American POWs in hand and a war which has been transmuted from US-Iraq to Arab-Israeli. It leaves the US with Iraqi-held hostages, NO access to the theater of operations except through Israel, and a whole lot of surrounding countries which will be undependably neutral at best.
At that point, it's hard to see how the US could prosecute the war further, short of nukes.
Any invasion of Jordan would stretch his supply lines too thin. Those troops would be demoslished from the air, assuming that they don't surrender en masse to helicopters and the press corps. Remember his armor is marginal at best and his ability to fuel it is almost non-existant.