This really kind of expands on what an "organ waiting list" is and how they work (and why rich people like Steve Jobs get transplants quickly)...
When somebody who is an organ donor dies, the organs are removed and they have a very limited lifetime. Typically they are made available to local hospitals within a certain range. This means for a recipient they need to be able to get to an appropriate hospital within a very short period of time.
For most people, this means registering at a local hospital and waiting it out. However there is nothing saying that you can't register at multiple hospitals, even ones that are a significant distance away as long as you can prove that you can get to the hospital within the specified time period.
So rich people who need organs will register on multiple lists all over the country and then charter an aircraft to be on stand-by for when the call comes in, provided you are the next highest person on the list (according to scoring criteria).
So, given that the President can be anywhere in the country in a matter of hours, if he registered at multiple transplant centers and had the highest score at the time an organ was available, he would get it. Steve Jobs did the same thing when he got his liver transplant, he had to fly nearly 2000 miles to get it, but because he was registered at multiple transplant centers and had a very high score, he got selected for one in Tennessee and was able to travel there when notified.