In an interview with Today, Liam Neeson said that when he got the call for "A Million Ways to Die in the West," his one stipulation for doing the role was that his character must have "a very broad Irish accent." Neeson made this demand to co-writer and director Seth MacFarlane in response to a joke on the animated series "Family Guy" (created by MacFarlane) that poked fun at the idea of Neeson playing an American cowboy.
"His main character, the little fat father in 'Family Guy,' they were making fun ... 'Imagine Liam Neeson being in a Western. Haha! With that funny accent of his.' So when Seth called me to ask if I'd do ["A Million Ways to Die in the West"], I said, 'I'll do it on condition that I do it in a very broad Irish accent.' So he agreed." Neeson said.
Neeson's remark about "Family Guy" is referencing a scene in the show in which Peter Griffin (MacFarlane), the family patriarch, says someone will "be as hopeless as Liam Neeson when he tries to play an American cowboy." The show then cuts away to a fictional scene showing Neeson voicing a character in a Western whose American accent rapidly degrades into an Irish one.