Gideon Sarantinos reports in his blog on a seminar presented by Phillipa Burgess of Creative Convergence. She emphasized you need to have impact in order to be considered by the big studios for writing assignments (the same can be said regarding getting the attention of publishers, by the way). It sounds like a Catch-22: they won't consider you until you've had exposure, but you can't get exposure with them considering you.
Even ten years ago, that would indeed have been a Catch-22. The rise of the internet gives us more alternatives for getting into the spotlight. The ones Burgess mentions include a web series, viral videos, graphic novels, or articles. Some of these you can produce for no cost, some for relatively low cost.
Consider collaboration. If your idea would work well as a graphic novel but you don't draw, see whether you can find an artist who isn't a writer and wants a chance to show what he or she can do.
If you have an idea for a web series, find a director who isn't a writer, and maybe a producer as well.
See whether a local dramatic society has actors and others interested in collaborating on a web series.
The ways to get attention without spending a lot of money have increased--and so has the need to be creative in doing so and in drawing people's attention to what you offer.
(My book, Your Writing Coach, includes two chapters on marketing yourself--one covers traditional methods, the other guerrilla methods. You can get the book from Amazon or your other favorite online or offline bookseller.)