Sure, it's going to be possible. It ain't going to be fun.
My first "real" job after school paid $23K in Boston (in 1995.) It's tough to live off of that, but it can be done.
Just break it down. Figure $2500/month. You're going to lose maybe 1/4 of that to taxes (I'm guessing) so you'll net $1850/month. If you can pull off a rent of $850/month, you've got $1000 left over for food, entertainment, utilities, transportation, etc. Get a roommate and that helps, especially when it comes to saving. (I had $430/mo in undergraduate student loans to pay off when I was making $23K.)
I know I wouldn't want to return to living like that.