I’m not an expert on this topic, so please take these comments with a grain of salt:
1. The simplest way a budget impasse could start is with internal feuding within the Republican Party. Some Republicans are very aggressive deficit hawks all the time. Some Republicans are only “deficit hawks” when a Democrat is president, but they spend freely when a Republican is president. Note that almost all of the largest budget deficits since 1990 have been under Republican administrations (Covid years under Trump and Biden were wonky and should probably be asterisked). So the pork-seeking Republicans and the deficit hawk Republicans can get into a stand off about what the budget should be.
2. Even if Congress is on the same page, Trump can choose not to sign the budget if he doesn’t get his pet issues addressed. This may seem like something that they should be able to work out beforehand, but his “priorities” change, sometimes daily, often based on who he happened to have spoken to last.
3. Some republicans want the government to break. The playbook here is to break the system in some way, point out that the system doesn’t work, and then make attempts to privatize that system or massively overhaul that system (likely with massive cuts of workers and largesse to contractors). It may seem odd that an elected official strives to make the government not work, but they are able to make that tack work for them at the polls. I think that this is a deep (and warped) issue that is hard for me to explain well.