I hope most teams have learned their lesson about rolling the dice and keeping only two quarterbacks on a roster.
An article by Mike Wilkening on ProFootballTalk discussed the Packers coaches struggling with that decision: keep two or three signal callers?
And they should know the seriousness of that call.
Last year, the Packers season suffered a serious blow when Aaron Rodgers was hurt and missed several games.
The backup situation was made worse in that none of the three training camp QBs were on the opening day roster.
Management was then scrambling in trying to solidify that position--and as expected, it did not turn out so well for Green Bay.
If it were me, I would find an approach to keep three QBs. Be creative and identify someone else who can do two things and strengthen the roster that way.
I think the NFL could help as well, and offer some sort of extra QB roster slot that does not count against the standard number. It could be a developmental QB or whatever, but at least it would improve the play on the field for fans--ones that will be shaking their heads if a QB goes down.
Just have three at your disposal.