The organisation recently spoke out against the forthcoming comedy, which stars Justin Bartha and Andrew Rannells as a gay couple who enlist the help of a surrogate.
Ellen Barkin plays the prejudiced mother of the surrogate (Georgia King), and does not want her daughter to carry the African-American egg donor's eggs.
One Million Moms released a statement saying: "NBC is using public airwaves to continue to subject families to the decay of morals and values, and the sanctity of marriage in attempting to redefine marriage."
Murphy told delegates at the Television Critics Association (TCA) press tour: "If they watched the show - I actually think they would love it. Because for the first time, they're represented.
"Ellen Barkin's (character) is a member of that group. Which is the truth."
Murphy, who is also producer of Glee and American Horror Story, says that his inspiration for the new show was Norman Lear's All in the Family.
"I think the show is funny, but I think in many ways the show is about tolerance and I think it's about a discussion of tolerance," he explained.
"And I think that their points of view are delivered with senstiivity and a certain amount of ferocity by Ms Barkin, so I think they would actually, if they watched it, they would like it."
The New Normal will premiere on September 11, 2012 on NBC.
Watch a trailer for The New Normal below: