First off, I wouldn't panic. As the SEO Moz blog recommends, don't just start trying to take a hatchet to your links and assume that that will fix the problem.
Second, realize that a lot of what is going on with Penguin is algorithmic. That may not be any comfort, but I'm currently being beaten by generically popular sites, not competitors. There's nothing I can do until Google decides that they want to value quality sites again over popular ones. Did they penalize us for some backlinks? Possibly (when we started SEO years ago we did reciprocals with exact match keywords, one of the things Penguin is targeting), but the lack of highly relevant results (as in the pages getting #1 are simply popular sites with a page that mentions those words, not sites focused on them) for our primary terms means that Penguin, like Panda, penalizes first and fixes later.
Third, unfortunately, the only way to plug the hole caused by Penguin (we're down 15-20% in traffic on our #1 site over last year) is to buy Adwords. Get a budget and start a campaign. It's the only quick fix out there. If it is links sinking your ship, even nuking them all immediately wouldn't fix your drop and will probably hurt you more in the long run. Go back to SEO basics (quality content and building good links) and hope this storm passes soon.