The Republic is not dead but it is in crisis mode at the moment and the Oligarchs, the fascists, the authoritarians that are desperately holding on to the idea of white, christian branded, hierarchical based society not that dissimilar to South Africa under Apartheid, want the republic to be effectively dead.
It's going to be hard to kill because of the courts, because of state governments, because of the press that is just starting to wake up to the crisis now. As i understand it, there are three other paths to his downfall that could happen.
1. The justice department, the FBI or even local Federal Law Enforcement (the US Marshall) could actually arrest him for a crime. That does not remove him from the office but it makes it extremely hard to carry on and govern.While, the AG Sessions, himself under criminal activity at present could head that effort of by firing the acting director of the FBI for instance. The strangeness and pressure from such an event would likely cause his own party to abandon him. If Pence were to be sworn in, he has his own set of legal issues around the Russia thing too.
2. Paper cuts - lots of investigations, lots of spotlight on the conflict of interests, the breaking of the law etc could bring him to the point where not only is governing impossible but the pain flows over and divides the Republican side itself. We have already seen evidence of this in several areas. That forces a resignation at some point and lots of back room dealing to make it work.
3. Despite all their efforts the Red side of the aisle realizes that there is electoral disaster facing them in 2018 and no amount of voter fraud investigations, voter suppression or gerrymandering is enough to help them fend of that disaster. They take control under someone like McCain and drive actual impeachment etc.
The thing is the people through resistance, the press because they realize their own profession is at stake and politicians who still believe they have a future would be bring so much discomfort to the current government that change would have to be made.