For FedEx Express I know you can, they are open usually all day on Saturday's...FedEx Ground is another question, it depends on if the destination facility is open. I'm in the same boat, mine shipped today from Carol Stream, IL and is scheduled to be delivered tomorrow by 3PM. I am only about 10 miles from Carol Stream. A lot of times FedEx Ground trucks are loaded on the weekends for Monday deliveries, so you may not be able to.
My plan is whenever I get the tracking numbers to notify FedEx to hold it at the FedEx Location so I can pick it up. The one it should go to for me is in Rockford and they are open until 7:30 Fridays, and 3:00 on Saturdays. It should make it from Carol Stream to Rockford by Saturday I think. Or I can just wait til Monday, I just don't like the thought of it sitting outside all day at my house. Stupid kids in the neighborhood have already been going through unlocked cars and took a bike out of my back yard(returned it, though).