The question would be whether Blair could hold his party together if he were to back a war by Bush which didn't have the backing of the UN Security Council, and went against the finding of the arms inspectors.

He doesn't have to have a vote in parliament to go to war, but at some point there'd be a vote where he'd be in danger of having to turn to the Tories to protect his majority.

But see this story for another reason he might be a bit hesitant.