@matthewc23 - You are correct and there are certain duties that the Governor has according to state and federal laws that allows them to intervene with Congress.
In most states the Governor is allowed to appoint someone to fill a vacancy and in reality they are legally allowed to fill the seat with anyone they see fit to be seated in that position.
I remember when Barack Obama was elected and his Senate seat was vacated, Governor Blagojevich of Illinois, had to choose someone to fill the vacancy and there was a rumor going around that he had the power to appoint himself and was talking about doing so.
Naturally the Senate would have found some way not to allow this to happen, but there was no law present at the time to prevent him from doing so.
This instance does show though that the Governor has the ability to appoint who they want in vacant posts in Congress and they could do so with an agenda in mind, say appointing someone of a particular interest group or political ideology.