You probably won't get anything now, at least the sort of position you're looking for. At this point, all the 2L summer associate positions are taken. Even if they aren't, you are eligible for that sort of position, since the Firms take 2L SAs w/ the anticipation of having them come in a 1st year associates after graduation and the bar exam.
You should send your resume out now, though, and you'll be way ahead of the game since 1Ls looking for the sort of summer jobs that you are w/ firms can't even send a resume until December 1. So you're still sort of ahead of the game in that respects.