Ten years ago, when I was in your position, I was offered the internship with Alaska, and I just could not pull the money together to do it. (At the time, the internship was unpaid.) Passing up the internship was one of the biggest mistakes I ever made in my career. After getting into the industry, I am realizing now how difficult it is to move from the regional to major level.
My advise, is if offered, do the internship. And put any and everything you have into the internship to make sure that you leave with an excellent reputation. It will pay dividends for you in the future..