I got my 2L job at the beginning of April, and my GPA was nowhere near what yours was. It was with the City Attorney's office--which is government (some would classify as public interest--depends on your definition).
Also, speaking from experience, if you are interested in public interest law, YOU MUST find a nonprofit to work for this summer. Even if it doesn't pay--it will broaden your marketability when you graduate. I had an interview with a nonprofit and the ONLY reason I was turned down is because my nonprofit experience wasn't long enough, and there were other candidates that had a lot more nonprofit experience. Nonprofits really like to see that you spent A LOT of time with a nonprofit. Six weeks and a semester (part time) wasn't enough, but a full summer, full time, would probably do it.
Dood, approx 20% of the 2Ls on my school's law review haven't found jobs yet (lower T1). It seems to be the beginning of the squeezed law employment market. try to find something, even if nonpaying, to do this summer which could still translate into a job next year. I would seriously doubt it's an experience issue as much as a "no one is hiring" issue. Hang in there and try not to let yourself panic or feel desperate.