It isn't that the Republicans don't care about deficits. They just care about their re-election chances more and that has been the case for some time now.
...and that adds up to not caring about deficits when a Republican is President.
We saw it with Reagan, Bush 41 and Bush 43. We also saw Obama get torn to shreds by Republicans over the huge deficits... even though they were caused by Bush starting two wars while cutting taxes -- who
does that?!? -- along with starting Medicare Part D without negotiating power, and the recession. We see it in repeated and often misleading denials that Bill Clinton presided over a budget surplus.
By the way, I disagree that Bush 41 lost the election because he signed a small tax increase -- that's a myth perpetuated by the rabid anti-tax wing of the Republican Party (aka "The Republican Party"). At the risk of oversimplifying, he lost because a) the economy was in a recession, b) Clinton was far more charismatic, and c) Perot likely drew more support from Bush 41 than from Clinton.
And now, we're going to see Trump propose policies that will create enormous deficits. I suspect some Republicans will care, but it's not clear if they will care enough to vote against a big fat tax cut for the rich, or repealing ACA taxes (mostly on the rich), and/or cross Trump on infrastructure spending.
And the truth is, we the people aren't keen on any spending cuts in our social security checks or cuts in government services we depend on or anything else that affects us directly. We sure think they ought to cut spending everywhere else though.
In the abstract, most people want spending cuts. When asked what people actually want cut, the answer is usually "almost nothing." The only thing people want to cut is foreign aid, which is only 1% of the budget.
Republicans have basically decided that they want to cut taxes, and don't want to cut programs, so they wind up borrowing massive sums -- or in Bush 43's case, creating enormous liabilities for his successor.
For me it is not cutting spending on those things people have to have. Where the spending cuts must come is in the enormous bureaucracy, government infrastructure, duplication, and black holes where nobody really knows where the money is going.
Yeah, there's a little problem with that. Namely, we know where almost all of it goes.
Everything except for the DoD / covert "black budgets" are extensively reported. Every department is required by law to explain its budget requests. Yes, it's a pain to sort through it all, but every dollar of spending is publicly accounted for.
FYI,
80% of the budget is Social Security, Medicare, Medicaid, unemployment, DoD, interest on the debt, and the VA. I'm sure there are some inefficiencies in those programs, but you're not going to slash the federal budget in half by rooting them out. And good luck to any President who says "I'm going to slash Social Security and Medicare and the Defense Department and VA."