Offer in federal consulting but determined to break into finance

Senior at a semi-target school who only recently decided I want to work in investment banking, so I have no IBD internships. This, in addition to poor networking, resulted in unsuccessful recruiting. Over the past few months, I have taken advantage of this website, bought and worked through BIWS, am currently working through Rosenbaum & Pearl's book, taking a free online accounting course, and plan on working through Damodaran's corporate finance class — basically, I'm working my ass off to understand the technical aspects of finance.

I was offered a job at one of the big federal consulting firms in DC and while that is a fine job, it's not what I want to do. I am looking for some advice on how to jump from federal consulting to investment banking. Do I turn down my offer and spend my last semester looking for work at a small firm? Do I accept my offer for consulting and start reaching out to people at BB/EB firms immediately? Being in DC is not ideal but I am willing to travel on weekends to meet bankers and obviously go for superdays.

tl;dr: senior with offer in federal consulting, want to work in investment banking. What do I do right now to make that possible?