With an internship, I think many companies may withdraw the offer if you start trying to negotiate salary with them. Though I disagree with it, as you said, often the attitude is that interns should be super grateful for any experience they get at all, and there are even some industries where interns are expected to work completely unpaid. And in my personal experience, the salary offered to me as an intern wasn't even negotiable, they just named a wage -- take it or leave it.
So I wouldn't try to renegotiate at this point unless one of the following is true:
- You're willing to take the risk of the company withdrawing the offer in order to get a possibility of a higher wage.
- You have a reasonable expectation that the particular company would not withdraw the offer just because you try to negotiate.
- The minimum number you gave is actually too low for you to be able to live.
Being an intern gives you a big leg up on getting a permanent position at the company. If they start talking about offering you a permanent position, definitely then would be a good time to renegotiate salary.