Regardless of your feelings about Bill Clinton's politics, he is a prominent, high-profile public figure, and an influential one at that. So why does he carry around those 'extra bags' under his eyes? Does he consider them a trademark?
It does not appear that he has prolapsed orbital fat, he just has extra skin (and possibly muscle) in the upper and lower eyelids. He would appear much less tired and more youthful if he had a 4-lid blepharoplasty. This procedure removes excess skin and/or repositions or removes bulging fat. Laser resurfacing, chemical peeling, or radiofrequency can help tighten some of the skin as well, but Bill would need surgery.
It may be that his cardiac history makes him a poor candidate for elective, cosmetic surgery, especially if he is on a blood thinner and is not able to discontinue it for several days. Until then, he will continue to look like he's in serious need of a supersized pot of starbucks.