Saddam's emnity towards Israel is well known. Capturing Jordan gives him a border with Israel and a base from which to attack. He will try to portray himself as the savior of the Palestinians, and by extension, the entire Arab world.
So... while I agree with the sigh and wish there was a way to avoid all this, I think we, as a nation, have to be prepared to protect our interests and our friends in the region, which happen to include both Jordan and Israel.
The problem with this analysis, is the IDF will attack Iraq the very moment they invade Jordan for 2 reasons: 1. Jordan & Israel have signed a peace deal; Israel will defend Jordan. 2. the IDF will, rightfully, consider such a move as an invasion of Israel itself.