Back then, there was still a sizable Blue Dog (conservative) Democratic caucus, I believe. So, Yes, I do think that Bush would have been able to get at least some of these Blue Dogs to defect and to support his tax cuts. Maybe they'd be able to secure some modifications for these tax cuts, but ultimately, I suspect that Bush is going to be able to get at least most of what he wants.
As for the Afghanistan and Iraq Wars, those two wars were bipartisan affairs due to the wave of both fear and hyper-patriotism that was induced by 9/11 and thus I still see both of these wars occurring in this scenario. Also, the Democrats likely lost the House in 2002 in this scenario due to GOP gerrymandering as well as due to the post-9/11 boost that the GOP is still likely to receive in this scenario.