Liasson is a graduate of Brown University (class of 1977) with a B.A. degree in American history. She graduated from Scarsdale High School in Scarsdale, New York in 1973.

Liasson was a freelance radio and television reporter in San Francisco before joining NPR in 1985. She was awarded a Knight-Bagehot Fellowship in Economics and Business Journalism to study at Columbia University Graduate School of Journalism for a year; she took leave to do that in 1988-89, then became NPR's congressional correspondent. She was NPR's White House correspondent from 1992–2001, during which time the White House Correspondents' Association awarded her the Merriman Smith Award for daily news coverage for 1994, 1995 and 1997. She is now NPR's national political correspondent.

She joined Fox in 1997. She is a regular contributor to Special Report with Bret Baier and a panelist on FOX News Sunday.

She is married to Jonathan Cuneo, a partner in the Cuneo, Gilbert, & LaDuca law firm in Washington, D.C.