Obviously, it depends on your standard of living and your circumstances, but you can do it for less than $2000. My partner is living on a $17,000/year stipend (about $1400/month), without summer income and while paying off loans, and he's still getting by fine - frugally, yes, but he still goes out to eat, goes to concerts, etc.
I spent four months after I moved to Boston living on $1600/month, and that included paying off two degrees worth of loans and maintaining a car.
Your rent will make a big difference. My partner and I each pay about $675/month in rent, including utilities. We do have two flatmates, but we live in Brookline in a quiet and very nice area. If you're going to live alone, then $1600/month will almost certainly not work for you. Like I said, it entirely depends on your choices and circumstances.