Dershowitz says that under Marbury/Madison the Scotus is the arbiter of anything between Congress/President.
A falsified or inadequate impeachment charge would definitely get the attention of Alito, Thomas, Kavenaugh, and Gorsuch.
It is entirely possible Roberts is a never-Trumper republican, but even he should see that the precedent for a political impeachment would mean every time an opposite party House gets in power that they would move to impeach a president over political differences.
Roberts and the SC will stay out of it.