I'm not sure either party tries especially hard to reduce spending. Clinton was strong-armed into abandoning expensive social programs in his first term and had a hell of a good bubble economy paired with a pre-Norquist tax regime and a post-base-closure budget to reduce the deficit in his second term.

I would say "look at the numbers," but the 2008 housing crisis and the 2020 pandemic really don't make for easy comparisons.

But by a first order of approximation, I fear your statement is correct. Tax cuts sometimes goose the economy but always increase the deficit. Democrats sometimes advocate for tax cuts, but Republicans always do, regardless of the current macro-economic climate.