The White House Press Secretary, who succeeded Sean Spicer in the role, frequently shuts down questions from the media and has been accused of repeating false information to journalists.
Miss Sanders invoked memories of a famous episode of The West Wing, which aired on television from 1999 to 2006, when she posted pictures of herself on Twitter with a Thanksgiving turkey visiting the White House for the traditional presidential pardoning.
The episode in question saw two turkeys locked in the office of the press secretary CJ Cregg, played by Allison Janney, overnight.
Miss Sanders tweeted: “We had a surprise visitor in my office today and got to live a real life version of an episode of the ‘West Wing’.”
Whitford, who played deputy chief of staff Josh Lyman and later chief of staff to President Matthew Santos on the show and was a vocal campaigner for Hillary Clinton, shared her tweet, writing: “I know C.J. Cregg. C.J. Cregg is a friend of mine. You’re no C.J. Cregg.”
Whitford will next be seen in Steven Spielberg’s new film The Post, which recounts The Washington Post’s handling of the Pentagon Papers in 1971.