Trump will probably fade fairly quickly. If he has any influence after he leaves office, it will be because he gets an ego boost from holding rallies, and a cash boost from campaigning. The test would be how Trump-backed candidates do in 2022.
But Trumpian politics is going to linger like the stench of that fish sandwich lost under the car seat in January as August approaches. He simply took advantage of forces at work in the Republican Party long before he first identified as a Republican.
Reagan campaigned as a populist and amplified the racist dogwhistles that Nixon used to capture Southern Democrats unhappy with civil rights legislation. Gingrich added the politics of personal grievance and obstruction to the party. And the Tea Party movement turned that into an inability to compromise and a cult of victimhood. Trump was good at taking that mix and turning it up to 11.
What Trump did not do was the work to build a movement that can function without him at the center of power. We will probably see others try over the next decade or so, but demographics are catching up to the Republicans, and they will either revert to a broader Conservative party or die out until a new party fills that vacuum without the baggage that comes with the party name.
To my mind, the next phase is going to be a huge fight among the right.
Trump, I assume, will eventually slope off to run his own equivalent of Mussolini's Republic of Salò from Mar-a-Lago, while trying to keep the donations flowing in from the faithful and exact revenge on Mitch McConnell and any other Republican who has colluded with reality and accepted the election result, trying to retain his grip on the Republican Party with a view to maintaining his fantasy of making a comeback in 2024, or one of the family so doing, while he pursues the idea of starting Trump TV and whatever else he dreams up to occupy his retirement.
However, Mitch McConnell is likely to take a view on this, having got what he wanted and banked his wins, in the form of judgeships, and he'd now like his party back from the crazy people, thank you very much. Meanwhile other rightists and grifters, whether related to Trump or not, will want a piece of the action, and I assume aspiring Republican politicians, particularly those who hope to reach the top, won't want always to be looking over their shoulder at an always unpredictable Trump and will want to be free of his constant demands for humiliating displays of public loyalty to the dear leader.
There are also, I assume, other Republicans who, like the Lincoln Project and the never-Trump people generally, who want a right-wing, small government, Republican Party, but who also believe in democracy, the rule of law, an independent judiciary and basic decency and standards in public life, and presumably want to restore the Republicans to something people other than cranks and crooks can support.
Add to this Trump's impending legal and financial problems, which won't go away, and I think the US Republicans are going to spend rather more of the next four years fighting each other, and rather less fighting Biden and the Democrats, than we're maybe assuming.