Struck out on all internship applications–am I doomed for FT prospects?

I'm a Math/Econ junior with a 3.8 at a school I've seen considered by most as a "mid-target" for consulting, but after applying to what feels like every firm in management and economic consulting under the sun, I don't have any offers for an internship for this summer, and I'm due to graduate next June. I have the option to do an unpaid experience at a small boutique in the Midwest, but given the cost of living in that area and the lack of external financial support, it isn't a realistic choice. 

I came into the process pretty late, originally thinking I'd want to go into academia or med school, and hence didn't join any of the business-related clubs that offer some guidance (they only take freshmen and sophomores), so I've had to learn most things on the fly. Is the fact that I don't have an internship for this summer an end-all for my prospects of getting into consulting after undergrad? If not, are there any recommendations for what one should do to productively fill the summer without an internship?