palm presser
1. slang A politician, especially one who makes a show of having a favorable public appearance (as by shaking hands). Sometimes hyphenated. The palm pressers that run our country care more about prolonging their careers than actually pushing through meaningful legislation.
2. slang Any person who makes a point of greeting, meeting, or socializing with a lot of people, especially because of some agenda or ulterior motive. Sometimes hyphenated. The conference was full of eager palm pressers trying to give you a sales pitch and foist their business cards into your hand.
flesh-presser
A politician, particularly one running for office and apt to meet, talk to, and shake hands with (i.e., "press the flesh of") many different people. There's no way you'll win the election if you aren't a flesh-presser with your constituents.