I would go for the .biz, though if I were someone else, I would go for hte .us. Only reason why I wouldn't go for the .us is becuase I don't live there :P
If its not business related, or US related and its tv show related perhaps .tv, or if unavailable .cc or .ws might be worth looking at. If you want to select just from .biz & .us I'd suggest .biz in preference as its not as geographically limiting as .us and you can push your site in a business direction if you feel that way inclined. I'm assuming that .net or .org are also unavailable based on your post.
I'm with omnia on this one, why not go for the .tv extension if it's a popular tv show? Neither .biz nor .us are well suited for tv shows, especially if the .tv exentsion is available.
Do I wish I had the .com? Damn right but sometimes one must settle and work harder to acheive. I fully expect to rank in the top 10 on googoo-gle within 15 months or less.
BTW the .info sister site is doing better and will bring the .biz along for the ride. </rant>
On topic -- is a tough decision -- I might consider the us or ws -- biz just doesn't feel right unless heavilly business related.
It's not too late yet. I would recommend going .ws or .cc, as those are rather inexpensive, but still easy to remember and with some branding should do the work.
If you're looking at a TV show then I'd go with the .us hands down when compared with .biz. However, I'd recommend just finding a new name if you're looking for an international audience.
You obviously don't find nor expect the kind of daily in-your-face traction with niche extensions like .BIZ. .BIZ was never meant to be used by the unwashed masses for their dog and pony show, just like Wall Street was never meant to be a Sunday flea market.
If being targeted and differentiated is your definition of "dying", then perhaps you may want to read the book "Differentiate or Die - Survival in the era of killer competition" by Jack Trout.