Your ability to negotiate is based on how much value you can bring to the company. As an intern you don't have much negotiating power (see related question).

Knowing I need the experience I said I was interested.

This quote leads me to believe that you don't have much software engineering experience (although you might be very experienced depending on your academic and personal work).

Your negotiating position also depends on if the company has other potential interns. If the company really wants to hire you they may be flexible. Software Engineering has a lack of skilled talent which gives you some but not much leverage.

Your options

If you are confident in your ability to do the work very well; you have 2 options

1. Ask if compensation is negotiable
   • Be prepared to justify why you are worth X amount
   • "Because that's the average" is not a compelling argument
   • If they say no, I wouldn't push them on this unless you feel that you have leverage
2. Ask if you can revisit the compensation issue in a month or 2 after you have time to demonstrate how much you are contributing.

I was in a similar position in my first internship (although I did have previous experience); I asked #1 and it turned out that they had a process for #2 in place already.