It would have been suicidal in '03. America was still smarting from Sept. 11, and the Bush administration was making (at the time) considerable arguments for invading Iraq, such as the yellowcake, the WMDs and the ties to Al-Qaeda. Yes, we know it's full of shit now, and a lot of people argued it was full of shit then too, but back then, the public was convinced Saddam had to go. Opposing that would have been suicidal. Much as the liberals argued the war was pointless, it only meant they were giving their opponents ammunition to paint them as weak-kneed traitors. And Hillary is nothing if not a political animal; she knows which way the wind is blowing, and while she might not support the war, she'll stay quiet. Come '05 and everyone realizing that not only did Iraq not mean the weakening of terrorism, but Al-Qaeda coming out stronger, that everyone realized the Bush administration played them for chumps, and it became safe to criticize the pointlessness of the war.
Kennedy opposed it, yet remained one of America's most powerful Senators until his death. Obama opposed it, and not only did he get elected to the Senate by a landslide but his opposition to the war was a major factor in his victory over Clinton. Clinton would come under intense criticism had she voted against it, but by 2005/06 she'd be proven right and win re-election to the Senate. If anything this strengthens her position in 2008 and makes it that much less likely she loses to Obama.
Over the course of the 90s centrist Democratic policy makers grew increasingly hawkish on Iraq. Al Gore hit Bush from the right in 1992 that they hadn’t put enough weight on Saddam’s sponsorship of terrorism.
If Bush didn’t have moderate democrats on board he wouldn’t have gone to war. The only way to get most moderate democrats to not back the war is for Saddam to act very differently post 911 as in don’t celebrate the attack and let in weapons inspectors in 2001 and give them access to his palaces.
And even after it became known that Iraq didn't have WMD's at the time of the invasion, former President Clinton had this to say in a 2004 interview with CNN:
"I have repeatedly defended President Bush against the left on Iraq, even though I think he should have waited until the U.N. inspections were over," Clinton said in a Time magazine interview that will hit newsstands Monday, a day before the publication of his book 'My Life.'
Clinton, who was interviewed Thursday, said he did not believe that Bush went to war in Iraq over oil or for imperialist reasons but out of a genuine belief that large quantities of weapons of mass destruction remained unaccounted for."