You would thus expect the debt to reduce in the hands of Republican administrations then if they were “fiscally responsible”.
It doesn’t.
No, administrations don't really make spending decisions. You'd have to say you expect the debt to reduce in the hands of Republican-controlled *Congresses*.
Which, to be fair, the last time the budget was balanced
was while Congress was Republican-controlled, but they haven't done it since.
Also, Congresses have spent years making it more and more legally impossible to balance the budget and reduce the actual debt since most spending is automatic and basically untouchable - good luck getting support to reform medicare/medicaid, the largest single expense, in either party. So we can also look at who reduces the deficit more, which I analyzed just now and found that, in general, Republican-controlled Congresses have posted significantly lower deficits within my lifetime than Democratic or mixed (one house each). That brief period of balance in the 90s is pulling a lot of that weight, but it remains true, if less so, from the 2000s to now. I didn't check whether Democratic Congresses do significantly worse than mixed, though.
Incidentally, interest on the national debt is now projected to edge out military spending as the third largest Federal expense this year, making it, for all intents and purposes, functionally impossible to ever balance the budget again. As of right now, interest makes up about 2/5 of this year's deficit. This is going to get worse as debt rolls over into the current high interest rates. There are signs that the market is slowly cottoning on to this, which will raise the cost of borrowing even more. So, that's exciting!
ETA: By the way, if you were wondering, according to the source I'm using for my numbers, defense spending currently comes in at just under half the deficit, social security at nearly 80%, and medica* at over 98%. These numbers, to be clear, don't sum to 100% because I'm comparing each spending bloc to the
deficit, not total spending - so it's a measure of how much you'd cut the deficit if you eliminated a spending group. Not that that would ever realistically happen.
(By the way, these numbers are using the officially reported budget deficit - for legal reasons, the actual deficit is slightly higher so the corresponding percentages slightly lower.)