No, he didn't. By insisting that a coalition of dozens of other nations get involved in the war, he basically guaranteed that nothing would really get resolved. The larger a coalition gets, the more "inclusive" its objectives become . . . and the more incompetent/ineffective it gets.
Bush 41 had no choice but to do whatever the U.N. wanted to do, since the U.S. had no formal (note that I did not say "legitimate") reason to even get involved in the first Gulf War other than to enforce U.N. Security Council resolutions. When you go to war on the basis of enforcing resolutions by an international body that has no standing in U.S. law, you have no right to complain when things don't go your way.
There's also been an intervening event (on 9/11/01, I think) since the first Gulf War that rather altered the landscape.
It only "altered the landscape" in that it gave the current Bush administration the political support to do something (i.e., invade Iraq and topple the Ba'athist government of that country) that it had every intention of doing anyway.
Good Lord.
Everyone knows he was busy planning Hurricane Katrina at the time.