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.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
n. a politician. Being a flesh-presser is risky during flu season. A palm-presser came to our door to ask us what we thought about his issues.
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.