In the last 10 years of fairly regular car rentals, I have never seen a manual trans car at any of the major in the US. If they did have them, I would think it would be most likely on some high end specialty sports car, rather than on the low to mid range cars as is typical in Europe and other parts of the world.
Not sure what your budget is, but this outfit:
http://www.exoticarexpress.com/exoti...rs_dulles.html
is likely have some sticks.