(Warning: the video contains, hmmmm, let's say, language you won't hear on network TV.)
Lowering of the lax high front vowel /ɪ/, where bit and bid sound more like bet and bed, is pretty widespread today across a variety of American dialects. Steve Conley on the Changelings list at The Ohio State University called attention to this YouTube video as a good example of lowering, which seems to be becoming "a popular affected pronunciation", particularly in taboo vocabulary. (Don't know him from Adam, but a big thanks to him and to those who passed this along.)
In addition to the socially-marked pattern of /ɪ/lowering here, this vowel change is also part of the Northern Cities Shift, and m[ɛ]lk has become a stereotype for especially southeastern Wisconsin. (A coda /l/ presumably plays a role here.) At the same time, lowering is stereotypical in the pronunciation of the state name Illinois ([ɛ]llinois). This last feature is likely older than NCS — I've heard it reported that the name was spelled with e in some historical sources.