That may have been what you did, but he ran on being a "uniter, not a divider", and promoted how well he worked with democrats in Texas.
So it would be reasonable that the average voter elected Bush specifically because he COULD get along with Democrats.
And he certainly did that the first few months, before Jeffords stabbed him in the back and then 9/11 happened and he realised the democrats weren't ready to do what needed to be done.
I think that part of the "strategery", implicitly, was that if he'd go along with some of the Dems' spending projects (No Child Left Behind, Farm Bill etc.) they'd not sabotage him/us on WOT, in Iraq and elsewhere, i.e. if Congress wants to spend some more money, let them be happy and leave me do the life-or-death stuff. They did sabotage, that's what they do. Like his father's breaking "No new taxes" pledge to appease liberals, both WOT/Iraq and spending were used against him (Iraq starting with Kerry's 2004 campaign).
You're exactly right.