In the end, when you go to a session, someone is going to point to you and say play. You have to execute quickly. You have to know what they want. You have to be able to play in a large variety of styles. You have to be very precise and feel very at home with a metronome/click track.
Here's a video of a Nashville session keyboard player and gives you a small sample of what it takes.
Lots of money to be made as a session guy but you have to be the best to make any money at it.