Bush cut taxes because he wanted to cut taxes. He had campaigned on a platform of tax cuts, and during the campaign, the rationale was that the government was running surpluses, and so the money should be returned to the people. After the recession hit, he switched to a stimulus rationale.
As for the spending, his two major spending programs were the Iraq War and Medicare Part D, both of which were unfunded. Medicare Part D was primarily a political strategy to shore up the vote from his base, but who knows? Maybe he genuinely thought it was a good thing to help old people as well. As for the Iraq War, before the invasion, the Bush Administration estimated that the war would cost maybe $90-$100 billion dollars, and that most of that cost would be recouped from Iraqi oil revenues. So, neither of these spending programs were an attempt at Keynesian spending per-se. That doesn’t mean that we can’t look at their effects to finesse neo-Keynesian models, but I don’t really see that there was any actual neo-Keynesian rationale behind any of Bush Administrations’ programs.
Keep in mind that typically in a Keynesian framework, the tax cut or spending intervention comes when the central bank’s traditional tools are no longer able to get traction in the economy (for example, when the central bank has hit the zero lower bound on rates). In the case of the dot-com burst, the Fed still had a lot of slack to cut interest rates, and they did start to do that. So, that’s another reason I wouldn’t label the Bush administration’s policies Keynesian.
Finally, in a Keynesian framework, you want to look the the multiplier effect of a particular government policy. Some tax cuts or spending programs produce more bang for the buck than others, and some programs can actually have a multiplier effect of less than one (which would be harmful to the economy).
So, let’s take the tax cuts. Tax cuts for the poor tend to have a good multiplier effect, because poor people tend to spend all their money immediately. Tax cuts for the wealthy tend to have lower multiplier effects (although not necessarily detrimental effects). If your goal is to get more bang for the buck, then you target tax cuts to the poor instead of wealthy. In Bush’s case, the tax cuts were across the board, with the actual dollar amounts being weighted heavily towards the wealthy. So, I wouldn’t call these tax cuts Keynesian in nature, because they didn’t try to maximize multiplier effects. It’s possible you can’t really get Keynesian tax cuts in our system for political reasons, but as far as I remember, the tax cuts that Bush ended up getting were pretty close to what he had proposed himself to Congress.
But, Medicare Part D, I think can be said to have good multiplier effects from a Keynesian standpoint (and on a policy level, I think it’s good to help seniors out with their medications). But as I said earlier in this post, I don’t think Bush was thinking along Keynesian lines when he proposed this program.