If 2/3 of the States vote to remove the president, then he must resign. The removal votes would all have to be within a certain time period, maybe two years.
You and I are thinking along the same lines. For example, one idea is the states grading the President’s efforts on border safety. Enough low grades result in a state-managed ‘impeachment trial’ where the verdict is guilty, not for ‘high crimes and misdemeanors’, but for a new definition of impeachment:
“poor job performance”.