An expression meaning "excuse me" but bastardized to incorporate the words "squeeze me"...
Mostly used to express surprise.
First recorded use in media was in the movie Wayne's World (1992)
Cassandra: Isn't that great? You've heard it?
Wayne: exsqueezeme ? Have I seen this one before? "Frampton Comes Alive"? Everybody in the world has Frampton Comes Alive. If you lived in the suburbs you were issued it. It came in the mail with samples of "Tide".