1. Polls can be misleading because they don't take into account intensity. Sure- people may say they are for or against something to a pollster- but it's the people who feel passionate enough to contact their representative and provide campaign donations that count. And it's people with money- like employers who employ illegal immigrants who really get their attention. In short- everyone has a voice- but some voices are louder than others.
And in this case, Americans were so fired up about 9/11 that they gave overwhelmingly support to whatever the president said was necessary. But now how many think the Iraq war was a good idea?
2. The UK has always been a strong ally and supporter of US policy. They owe us big for our help during WW-I and WW-II and could need our help again. More telling is how little support we got from other allies- who only sent small token troops leaving it to the US to do 95% of the fighting and spending. And the war was so unpopular among the British people that it ended Tony Blair's political career.
3. Even a ruthless dictator can do nothing when his own men are turning on him. A lot had changed since 1990- rebellious feelings had reached a point in Iraq where Saddam couldn't trust his own army. Note how they did almost nothing defend him during the invasion- most pulled off their uniforms and ran.
In the case of Desert Storm- we had overwhelming world support because there was no question that Saddam had broken international law. And Bush Sr did just what the UN resolution authorized- he ousted Iraq from Kuwait. He was authorized to do no more than that. In this case, most of the world saw us (the US) as the aggressors!