You need to read more about recent US political history. Presidents play a huge role in shaping legislation because of their veto power, the bully pulpit and party discipline. Abandoning his middle class stimulus for deficit reduction plan was a fundamental decision that Clinton made early in his administration. HW also deserves credit for backing off his pledge and raising taxes. His son’s tax cuts combined with the Iraq war and higher domestic spending wasted all the hard-won gains of the 90’s.
While I’m no fan of Bush’s fiscal policy, his power in budgetary processing was always very limited. I definitely do not agree with characterizing his influence over it as “huge”. Yes, he theoretically could have vetoed it. I’ve seen no evidence that he would have done so (he was never much for the veto). Nobody wanted to cut spending, so spending was not cut. I don’t excuse Bush for that, but neither do I pretend he was any different than everybody else in Washington int he last decade. (This attitude, IMHO, began in the last two Clinton years, as legislators realized they could spend Spend SPEND more More MORE, precisely because the economic growth had been so strong that wealth seemed abundant.)
The 2001 tax cuts were pretty close to what Bush wanted and played a large role in the subsequent deficits. The Iraq war has also played a big role and that was Bush’s doing. I believe Bush played a big role in the prescriptions drug bill as well which was the biggest piece of domestic spending. So he bears the lion’s share of the blame for the deficits.