Their attempt right now is 100% states' rights garbage---the Constitution gives the power of deciding how a state awards its electors to the state legislature. The goal right now is to throw up enough dust to give cover to states to not certify their election results, letting the republican-controlled-via-gerrymandering state legislatures simply choose their preferred slate of electors. There are problems in some states like Michigan where the state legislature has previously passed laws explicitly laying out how the state awards electors, and it can only be based on the outcome of the popular vote in that state. The longshot idea would be that these GOP-controlled legislatures would pass a new law giving them power to appoint in the scenario where the election isn't certified. In MI and PA and WI, the Dem governors would certainly veto, but then you take it to court and see if the GOP judges will go along with an insanely stupid reading of power vesting in state legislatures meaning that they don't need the Governor's approval to change the method of appointment.
A lot of this is going to go down in flames when GA certifies within an hour or so. The GOP SoS stepping up there and very clearly dismissing all of this nonsense was an important and, for his own political future, brave move.