IMHO you should never repeat songs at the same gig unless requested to at the end of the night. Wait till you can play four 45 minute sets.
Reason being, if you were a club owner, would you hire back a band that couldn't do this when you can hire a band that can and will? Dont forget, there are few places where there are a shortage of cover bands. Competition is rampant everywhere, and if your in a cover band, you will be compared to the rest of them whether you want to be or not.
No matter your skill level, experience, how serious or not serious you are about playing, when you play out you are representing yourself and your band. Repeating a set comes off as lazy, mediocre, and unprofessional. Plus if you tried to stretch out your two hours of music by taking breaks, you would have to be on break for the same amount of total time you would be playing. Would you pay to see that?
If your worried about being able to get more tunes down in time for the show, just throw some old standards in there to cover time, like one of the previous posters said..
Some rare exceptions:
A. Its a free show and you dont care.
B. You really don't care if your asked to come back.
C. Literally 0 of the same people who heard the 1st set are still there. (including bartenders ect.)
D. Some drunk requests a song you already played (assuming said drunk wrote it on a 5 dollar bill, bought you a beer, or its his/her birthday).
E. The audience is rude and you want them to hate you.
F. Its the greatest song ever written and it must be played multiple times daily

Your singer is right. Throw together some extra tunes, do your best, and have a good time.