Has anyone done much work subbing for a larger firm as a self-employed independent consultant? I had some gigs a few years ago that were all because of previous connections I had. However, I'm thinking of finding some work now by sending unsolicited "bids" (i.e., resume, cover letter, maybe portfolio) to several firms asking if they could use a cheaper subcontractor.

Does anyone have experience doing this? Is my approach the right way to go or completely way off base?