Definitely the phoenix; below the circle is an upward-pointing triangle which represents the flame by which the phoenix will destroy and renew itself every century.
It looks like the phoenix used in old Russian medals. I would suspect that it symbolizes the resurgence (they hope) of Russian style communism. Personally knowing the Clinton's biggest backer and some of the connections they have, I can attest that they aren't liberals, they aren't simply old style left leaning democrats, they aren't socialists. They are out and out communists.
The father of the man that made Bill Clinton was one of the founders of the US communist party... and the family business continues. Hint for the insiders: His company's stock certificate featured a hammer and sickle. Not Tyson and not Armand Hammer.