The short answer is that you've missed out on your best shot at consulting internships. Its worthwhile now to initiate contact with your school recruiting office, recruiters at consulting firms that come to campus, etc - and explain your situation in brief with a resume attached.
At the same time, I'd look into alternative summer employment options - while helpful, it's not mandatory to have a summer consulting internship for fulltime recruiting (there are very few of these to begin with).