There are alot of independent traders on the floor who just have a seat and trade their own capital or are part of a proprietary trading firm. Some are legit, some are sleezeballs who will wash out, but in this type of environment there are still some old school people who would rather have a clerk with street smarts than someone with book smarts- i.e. do what I say, take all the crap I give you, etc....I think alot of them feel that the kids comign out with finance degrees have too much of a sense of entitlement. On the other end of the spectrum are places like goldman sachs, etc, where they want to hire traders with PhD's and tons of book smarts.
So yes it is possible, but if you get that kind of job you are going to get shit on and it will take a little while to make "wall street" money...alot of those types of positions start between 20 and 40k with a bonus if you do well. Check out craigslist, you will see the occasional ad for entry level clerks on the different exchanges. Keep in mind that the floor is dying....you would probably be best served waiting out the current downturn by going back to school and getting your degree.