Well, when I was stationed at the National Naval Medical Center in Bethesda MD, President Reagan and his wife came in for their annual physicals, and, although I was not personally involved, I can tell you that it went something like this.
Marine One landed about 4:00PM. (This I know because I had just returned to my barracks room after my shift, and the barracks is right near the helipad.)They Reagans were conducted via ambulance through a cleared area of the Emergency room. Admission work, blood work and x-rays were done. They were then ensconced in the Presidential Suite (Yes, they actually is a whole suite set aside for the President's use, but occasionally it would be used for extremely high ranking VIPs.) The Suite has almost everything needed to do a complete work-up. The main reason for passing through the ER is that it was connected to radiology, so chest x-rays and, in Mrs. Reagan's case, a mammogram could be done. I believe they then had EKG's done. Somewhere along the way, urine was collected. Dinner was served, then, like any other patient, only with a lot more luxury and protection, they spent time probably watching TV until they went to bed. (What they did is purely conjecture. as I said, I was not privy to the actual exam.)
The next morning, they were subjected to complete physical and dental exams. They may have had colonoscopies done that morning, or that may have been done at the White House. (The clinic there is equipped for everything from a paper cut to minor surgery.) About 12:00 noon, the Presidential limo, which was driven in that morning, took them to get their eyes examined. (The limo was brought in because the eye clinic was in a separate building.) About 2 hours later, the limo brought them to the helipad, where the back-up chopper had been brought in. (Just in case someone managed to slip past the Marines guarding the one they first arrived in. Also, it is standard practice to fly 2 birds so that would-be terrorists wouldn't know which one the President was on.) They re-boarded Marine One, and they, the secondary bird, and the limo all returned to the White House.
I remember it so clearly because when they built the Hospital at Bethesda (affectionately known as "FDR's last erection" because the tower of the old part of the hospital was built then) instead of building a hospital and then putting a golf course on the grounds, they built the hospital on an existing golf course, and you couldn't gold during helicopter operations because the pad was right next to the 3rd green.
After all that, I guess the short answer would be that the President should go through the most extensive physical exam possible.