A better idea would be to require that Electoral votes be counted by House District (except for your 2 Senate votes, which should still be counted by popular votes in the state).
That way, subsets of a state could vote against the state as a whole; Austin, TX could vote D, east California could vote R, etc.
This is probably also legally doable by Congress without an amendment; it also keeps the strong-and-broad support the Electoral College requires (which is better than the Strong support a majority-only system requires). It also isn't an invitation to fraud/gamemanship, as TFA's proposal is. (well, gerrymandering would still apply, but that's a separate problem that needs work anyway).
It would also reduce the number of Florida 2000 debacles (since you'd have to be within about 2 EVs of the other guy to need a state-wide recount).
For added bonuse, senators could be done the same way in states with at least 3 districts.