Well usually the kicker/punter, or people who have played quarterback in highschool, college, ect.
Usually the kicker or punter will come in at quarterbacks. But the event of all three quarterbacks getting injured in one game is very rare.
Charlie Batch, Dennis Dixon and Byron Leftwich all served as backup quarterbacks in 2010 for the Steelers. Dennis Dixon was put on injured reserve after week 2.
The 1982 Denver Broncos had three quarterbacks on the roster: Steve DeBerg, Craig Morton and Mark Herrmann.
Generally, a team will carry three quarterbacks on each of its game. Only one quarterback plays at a time but more are on the roster in case of injury.
The Patriots had three quarterbacks in 1990: Marc Wilson went 0-6, Tom Hodson went 0-6, and Steve Grogan went 1-3
You could but it would be very risky. I have seen games where both quarterbacks were injured and the team had to use a running back to finish the game (Washington/Philadelphia, 1990 ... the 'body bag' game). I can't say that I know every player on every NFL roster but I can't imagine there is a team that carries less than three quarterbacks on their 53 man roster.
Missouri
Three (3)
After Troy Aikman's retirement, four quarterbacks started games for the 2001 Dallas Cowboys: Quincy Carter (eight starts), Anthony Wright (three), Ryan Leaf (three) and Clint Stoerner (two). The Cowboys ended the regular season with a 5-and-11 record.
Notre Dame, Alabama, University of California
mcnair's one for sure
Carson Palmer
19 players and up to three quarterbacks.