Support for it was very wishy-washy in both the general public and Senate before it began.
Today marks the 10th anniversary of the end of the Persian Gulf War, when U.S. and allied troops forced the Iraqis out of Kuwait and a cease-fire was declared. According to a new Gallup poll, conducted February 19-21, as Americans reflect on their country's participation in that action a decade...
news.gallup.com
As I mentioned earlier, Congressional testimony by a Kuwaiti girl that was demonstrated after the war to be completely fabricated played a not-insignificant role in changing public opinion into supporting removing Saddam from Kuwait. The public and the rest of the world really had to be convinced into supporting that war, for the reasons I mentioned earlier (i.e., it wasn't a clean "they attacked us so we're going to attack them" deal).
If Desert Storm ended up heading south like Afghanistan or Iraq Part 2 did, it would have been a very politically divisive and eventually immensely unpopular conflict, just like the other 2 ended up being (and were both broadly publically supported before they began). It ended up being a very successful operation, so the criticism of it initially kind of ends up being forgotten. I don't think that war was successful because it had broad public support; it (ended up) having broad public support because it was successful. It's not altogether different from fans jumping on the bandwagon of a successful sports team, or a fan yelling "no no no!" before a basketball player jacks up a wild, contested 3 then cheers "yeah, great shot!" after it goes in.