I don't see any reason why Brewer won't veto this. She has no reason to fear pissing off the far-right since she's term-limited, and she's too old for presidential ambitions.
By the same logic, she has no reason to fear pissing off moderates. If she truly believes she won't be running in any future elections, she can make whatever decision she wishes without worrying about the politics too much.
I've seen her as the type to use the far-right to get elected then ditches them afterward. Just look at the heavy handed tactics she used to expand Medicaid. Even many Democratic governors wouldn't go that far.
