There are places online that if you submit your design, they will make a number of items for you as long as it isn't a copyrighted item, such as Zazzle. (see link below) There are other places too. This is just the first one I thought of.
These places places will make them and ship them without a person actually having to place an order and then keep all the shirts in their house and such. And the beauty is, they make more than just t-shirts. See, I am relatively positive I would never wear a tshirt, but I would buy a coffee cup or a hoodie or other things.