Correct... and, here's another little fact you won't here repeated often: There were actually MORE (in numbers) countries involved in the second "coalition of the willing" than there were in the first. Because France and Germany (who were being paid off by Saddam) didn't join the second venture, the Left declared it a "unilateral" decision.
I'm not disagreeing with him but Bush Sr. wanted war and tricked Saddam into thinking he could have Kuwait. Before the invasion Bush had his diplomat tell Saddam that the dispute with Kuwait was considered a border dispute that the US had no interest in. The US reaction after Saddam's invasion was a complete surprise to him.
I remember when Bush Sr. pulled his punches and did not march into Iraq to get Saddam the Democrats let him have it, saying the military should have continued on and finished the job. If the president is a Republican then no matter what decision he makes the Democrats will take the opposing point of view. If GW Bush suddenly came out for nationalizing the health care industry the Democrats would suddenly be vehemently against it.