Firstly, Birth Control is already free if you're on welfare. Making it free for everyone wouldn't reduce the number of people on welfare.
Second, Birth Control isn't expensive. You can get generic Ortho-Cyclen for 12 bucks or less for a one month supply. (Those damn evil drug companies are charging 12 Junior Bacon Cheeseburgers!!!!)
Third, Depo-Provera needs to be used much more often in the welfare community. Its a once every 3 month shot that prevents pregnancy. If you want welfare, you get the shot.... Can't "forget" to take the pill this way.