I think Orton could be ready to play by week 3...he's gotten ready that quickly before on a new team.
Kansas City picked him up in the later part of November in 2011. Three-and-a-half weeks later he started, and the Chiefs beat the Packers, who were on a 19-game winning streak. Orton did pretty well too...threw for 300 yards. He started the final three games, where the Chiefs went 2-1.
I think he'd be up to speed enough after the first 2 games.
Picking up Orton is probably the best move the Bills could realistically make at this point IMO. Not that he's "all that," but he's a solid backup that you know can step in.