Remember 2001, when the federal government was projecting huge surpluses, and people were worrying what we would do when the government debt was completely paid off? Well, it looks like we solved that problem!*How did we do it? The table above, from economist J. Edward Carter based on CBO data, shows the causes of the change from a ten-year surplus of $5.6 trillion to a ten-year deficit of $2.9 trillion--a swing of $8.5 trillion. The biggest factor was increased spending, of which increased defense spending was the largest piece. The second biggest factor was changed economic and technical assumptions (that is, the forecasters were wrong).
The tax cuts amounted to $1.8 trillion of the $8.5 trillion--about a fifth. [Update: As several commenters point out, the added debt service is partly attributable to the tax cuts. The simplest correction would be to focus on the primary deficit by taking out the change in debt service. In this case, the budget swing is 7.2 trillion, of which the tax cuts represent a quarter.]
Even that amount is most likely an overestimate, because it relies on static assumptions. A dynamic analysis that allows for a feedback of lower taxes to more rapid growth would reduce the share of the budget swing attributed to tax cuts.
Reasonable people can disagree about whether the Bush tax cuts were advisable, but don't let anyone tell you that the tax cuts were the main reason the surplus of 2001 disappeared.
* Before some commenter flames me: yes, this sentence is tongue-in-cheek.