Woody Harrelson's late father Charles Harrelson was a Texas hitman who had famously claimed to have killed President Kennedy (he was sentenced to life in prison for murdering a Texas judge), but later admitted that he made up the story.
In an interview on Jimmy Kimmel Live! (2003), Woody Harrelson said he called Bryan Cranston and asked for advice for the role. Bryan Cranston was also shooting his own Lyndon B. Johnson movie All the Way (2016) around the same time, and Cranston helped him by giving him advice and putting Harrelson in touch with people who knew Lyndon B. Johnson.
The "LBJ ordering pants" scene is taken almost verbatim from an actual audio recording of that phone call, available widely on the web.
Former President Lyndon B. Johnson is one of four people who have served as President and Vice President, as well as in both houses of Congress.
Woody Harrelson had to undergo two hours of make-up application each morning, and one hour for removal in the evening.