Yes. The Republicans are not and never have been united around fiscal conservatism. Eliminate-the-deficit libertarians are one faction within the party but not the dominant one, and Trump doesn't come from it. Same with most right wing parties the world over: the bigger faction is usually one that likes both tax cuts and spending increases. That's why deficits are out of control across the west: between the tax-and-spend left and the don't-tax-but-spend right, the don't-tax-and-don't-spend contingent isn't big enough to outvote the others. Clinton was very unusual in this regard, perhaps a product of the short post-USSR consensus.
Elon is a libertarian and has been allowed to go do some spending cuts around the edges. This gets support from Republican members of Congress partly because the USG turns out to be spending a lot of money on highly partisan Democrat projects, but mostly because it's someone else doing the cutting and not them. Even if they know they should be doing it themselves they don't want the crazies trashing their cars, so if some outsider does it for them that's a deal they'll happily take whilst it lasts.
All that said, it's inevitable that the administration would be blowing through more money than before even with DOGE. It's the nature of debt that it compounds. The level of cuts required to even keep the deficit stable would be huge because interest payments are accelerating, and the cuts DOGE are allowed to make are small (even when they go further than they might technically be allowed).
Right now there's just no mainstream support in US politics for serious austerity. There never is in any country, but sometimes the public can be convinced to agree to some amount if politicians do a good job of communicating the deficit problem. The UK in 2010 is an example of that, where the Conservative/Lib Dem alliance was able to convince the public to vote for spending cuts (albeit not as deep as were actually required... but it tided the UK over until the economy started growing again).