The more and more I look into all this the more and more I feel dirty but wish for an actual moderate (in US terms) Democrat President and a majority Republican led congress.
There's no good rhyme or reason you can find with regards to the debt and Presidents over the past 6. The closest thing to consistent is that all three of the last Republicans had the Debt go up under them. However Reagan's deficits lowered, then Bush I's went up, then Bush II the Deficit went up, then down, then back up. Meanwhile on the Democratic side you have one who has had a steady rise in both debt and deficit, one who had a steady decrease in both, and one who has a mild increase then decrease then increase. There's no real honest and good indication you can get strictly by President.
The congress and debt, that's a different story. Save for the 4 years at the start of my sample (77-80), whenever we have a Split or Democratic controlled congress the Debt has relatively maintained or risen. Every time we've had Republican Control (outside of 2002) we've either relatively maintained or lowered itself.
Additionally, ground wars seem to be a better indicator for higher deficits than the control of the Presidency or the House. After Grenada and Lebanon Reagan's deficits lowered a bit, before Panama followed by Desert Storm occured and it went back up. Clinton's defies this a bit, but a large portion of Clinton's actions (Bosnia, Kosovo) were more focused with air support than full on ground war. Under GWB, during the start of afghanistan and iraq we have a raise, while it lowered a bit as the major combat lulled and then rose again with the surge. Similarly, with the surge in Afghanistan we've been seeing an increase as well.
For all the talk of Presidents, I think its a bit misguided. Wars and Congressional control likely has far more to do with these things than whatever guy happens to be in the big chair. That said, whose in the big chair is largely responsable for the Wars so there is a legitimate thing there. But in regards to debt, I think Congress is a far better indicator and its not shocking in the least to me that the best years this country has seen in the past 3 decades with regards to the debt and deficit came at a time where a Democratic President specifically tried to lean significantly more towards the center and Republicans controlled the congress.
Federal Debt as % of GDP
Federal Deficit as $ of GDP