Agree with what's been said. Depends on the genre of music, the lineup in your band (sax, keys, Peruvian Nose Flute?), and who you see as your target audience. Might be ballads, rockers, funk, etc. some gigs draw punters who want only songs they know (this depends greatly on the age of the punters - "Who's Paul McCartney?" -What's Greenday?) - other crowds are there to listen to 'originals' . I'd suggest befor learning a million songs and attempting to become a human-jukebox, you/your band, need to give thought to who you're likely to be playing for, where/why you're playing -a dance, pub, background music, etc. - and what you are trying to achieve. If you know the film, you'll remember when the Blues Brothers ended up playing 'Bob's Country Diner'. Your band may be superb in some contexts and struggle in the wrong environment. As said by Paul above, you'll never please everybody. Focus on your 'target' and you should avoid becoming the 'square peg in a round hole'.
i distinctly remember, years ago, an unscrupulous 'agent' sent our 'west-coast American' soft rock band to play in a venue, which turned out to be expecting an accordion player and snare-only drummer. As we unloaded a full Transit load of gear, I had a feeling we were in the wrong place. The average age of the audience must have been 60+, so we spent the evening working, not as a band, so much as a group of individuals, coming together in various permutations to provide everything from folk songs, to numbers best described as 'easy listening'. We got away with it, just, but had we been more thorough in ensuring the right genre in front of the right audience, the stress levels would have been much, much lower. Hope this helps you in some way?