They could've paid off debt like good fiscal conservatives are supposed to do. As for causality...
The surplus was 2.3% of GDP in 2000. With the dot com bust and 911, it dropped to 1.2% in 2001 as unemployment increased over the year from 3.9% to 5.7%, causing revenues to decline by 1.1%, while the spending share was constant. The tax cuts went into effect in 2002 and we're phased in over several years. Unemployment went up slightly over the year from 5.7 to 6%. The budget went from a 1.2% surplus to -1.5% deficit, a swing of 2.7%. Revenues fell from 18.8% to 17% (-1.8% with personal taxes 1.5% of that) and spending increased by 0.9%. The tax cuts alone would've created (caused) a deficit in 2002 since the unemployment change was minimal.
As the phase-in was accelerated in 2003, the revenue share fell from 17% to 15.7%, and the deficit worsened from -1.5 to -3.3% of GDP. The tax cuts were the most significant "cause" of the larger deficit, as the personal revenue share fell by 1%. So, I'd say they sure as Hell were causal, since the unemployment impact mostly occurred in 2001. I would add that increased spending was contributory.