The White House says Rice was only following their talking points based on the best available intelligence at the time, but McCain and Sen. Lindsey GrahamLindsey GrahamTrump: 'I hope' Russia is able to get Clinton's emails Syria activists cheer Kaine pick Vulnerable GOP senators praise Kaine MORE (S.C.) have accused Rice of misleading the public.
Rice is rumored to be a top candidate to become Secretary of State when Hillary ClintonHillary Rodham ClintonTrump: I wish Ivanka and Chelsea Clinton weren't friends Poll: Clinton up by 6 nationally Romney: Trump victory 'very possible' MORE steps down, but McCain and Graham have said they would oppose her nomination.
McCain said on Sunday that he would "give all nominees the benefit of a hearing process."
But he added that Rice should go back on "Face the Nation" to explain that she gave the wrong information to the American people.
"That might be a beginning," McCain said.