Fauci was referring to the date supporters of former President Donald Trump, of whom Cruz is an ally, stormed the U.S. Capitol.
Appearing on CBS's "Face the Nation," Fauci was reminded by host Margaret Brennan that there are "a lot of Republican senators" taking aim at him.
Fauci's response: "That's okay. I'm just going to do my job. And I'm going to be saving lives, and they're going to be lying."