It is true and shameful that most centrist Democrats (most Democrats holding federal office are centrists) supported the attack on Iraq. I suspect many, possibly most, knew better but were afraid to be accused of being "soft on terrorism." Others may have believed the administrations disinformation. They are not as guilty as the members of the Bush II administration who had access to much more information than the legislators.
If you closely read the Bush II admin's statements on WMDs and the connections to 9/11 you can see that very few, if any statements were outright lies. Most of the statements were carefully parsed to give the impression of certainty about the WMDs and 9/11 connections, without actually stating so as a fact. A famous example is Rice's "smoking gun is a mushroom cloud" statement. That careful parsing tells me that they knew they were lying and/or could be wrong.