How does one go about getting a small press magazine picked up by a national distributor?

I've been publishing literary magazines with smallish press runs for a few years now, mainly selling them through consignment at local bookstores, ad trading with other small magazines, at literary events, etc. I think it is time to expand into at least regional distribution. I've called the local distributor in my area, and the man claimed that it could not be done. That I had to call every store and get permission for my magazine to be sold there.

He has to be lying. I'm extremely skeptical that Poetry called up Boardman Book and Smoke and did this. I doubt they've heard of Boardman Book and Smoke.

Does anybody have experience with distribution? What companies do I contact? How do I make my pitch so that I'm taken seriously? I'm not putting out something xeroxed at Kinko's and stapled together. This is glossy, book-bound magazine with very strong content.