Virgin America Elevate - Ticket but no seat

I just bought a ticket on Virgin for BOS->SFO on 8/25/2011.

However -- there were no seats! None, except First and Plus/Premium (forgot the name). Couldn't choose one of those except for an extra fee.

Do they just assign me a seat in the airport? I'm Virgin (Atlantic) Flying Club Gold, doubt that matters here, but hoping I get a good seat and not the middle seat in the back of the plane...

Certain rows are available for airport assignment only (see the FAQ at the top of this thread). You want to ask for row 4. Get to the airport early, before non-revs get there. They tend to give them row 4.