There are a number of issues to address, but let me start with this, from the 14th Amendment:
But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the executive and judicial officers of a state, or the members of the legislature thereof, is denied to any of the male inhabitants of such state, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such state.
The issue of a state LEGISLATURE ( more anon) designating a slate of electors became quietly an issue in 2000, when Tom Feeney, then the Speaker of the Florida House, starting a movement to legislatively designate a slate of electors for George W Bush. As I recall, Scalia saw that if that happened, SCOTUS would have to rule if a case were brought about stripping Florida of its House representation for violating this provision of the 14th Amendment. That was part of the rationale for stopping the recount because if the recount continued and showed Gore winning Florida and yet Bush got the electoral votes (which in theory the legislature had full power to do), then it would have delegitimized Bush’s “victory”.
But at least there, absent the recount, the official results showed Bush ahead by 537 votes.
In ALL of the discussions about state legislatures doing this now, I see no mention of this black letter constitutional language. Imagine that Trump pulls the legislative coup in MI, WI, PA, AZ, NC, and FL — all states with legislatures controlled by Republicans. That would further reduce the Republican share of the House of Representatives, because all of those states are gerrymandered to produce more than reasonable Republican representation.
One more note on this, before I change focus to the courts. Governors have NOTHING to do with this. It is the province of the state legislatures by themselves, the same way approval of constitutional amendments is. Thus the top-rated diary is not accurate on this point. As to whether state legislatures can even act, that depends on what the states’ constitutions say about sessions. I have not researched if any of the four states with D Governors either have scheduled session where such a coup could occur, or if the legislatures can come into special session without being called by the Governor.