Physical Danger
On a day-to-day basis—no, not at all. You have a zillion people around you making sure you're okay, that everything is safe, that you're comfortable, that you're not getting sick, and that there are no nails sticking up out of that board over there. But the potential exists for some real serious danger.
If some nutjob gets it into his head that you'd be better off dead, you could be a goner. You're followed everywhere by highly-skilled Secret Service agents, but even they aren't super-human. If they can't get in the way of a bullet, there's no turning back time or feeding you the fruit of everlasting life. To date, there have been forty-four U.S. Presidents, and four (Lincoln, Garfield, McKinley and Kennedy) have been assassinated. For you math-haters out there, that's one in every eleven. Those are not good odds.
Another thirteen (Jackson, Hoover, both Roosevelts, Truman, Nixon, Ford, Carter, Reagan, both Bushes, Clinton and Obama) have survived assassination attempts. (Some of those attempts had less of a chance of success than others. In late 2011, one brilliant gentleman fired shots at the White House while the President was in Honolulu. Maybe he was hoping for a lucky carom.)