Sure you can. You just have to play an average of 3 or 4 nights a week, every week. You also have to be really, really good and really, really flexible. You have to be literate as a musician, though many people refuse to be. Reading and writing music is absolutely necessary if you want to make a living unless you're extremely lucky. It also helps to live in a metro area of at least 500,000 or so. You need to be good enough that you get called when any show is coming through your town and they need local musicians. You'll probably need to be in a great cover band that has a consistent Wednesday or Thursday night gig at a popular bar. If you or someone in your "main" band is a great songwriter, you might even make a few bucks playing original music. You're going to have to be in several groups and generally refuse to play for free unless it's something you're just dying to do.
Basically, a musician can make a living, they just have to work their ass off to do it and won't always be playing the music they love, just like any other job.