The teen father of the infant grandson of the former Republican vice presidential candidate and former Alaska governor made the remarks in Part One of an exclusive interview with "Early Show" co-anchor "Maggie Rodriguez," which aired Wedesday. Part Two aired Thursday.
Johnston, 19, told Rodriguez he doesn't plan to reveal what he knows about Palin, who quit as Alaska governor in July.
Johnston lived in the Palins' house for two months while waiting for the baby he has with Palin's 18-year-old daughter, Bristol, his former fiance, to be born.
In Part One of the interview, Johnston also repeated a story he had told to Vanity Fair magazine -- that he heard Palin jokingly refer to her baby son, Trig, as "the retarded one." Trig was born with Down syndrome.
"The Early Show" asked Palin if she had, in fact, said that.
In a statement, Palin said, "We have purposefully ignored the mean-spirited, malicious and untrue attacks on our family. We, like many, are appalled at the inflammatory statements being made or implied.
"Trig is our 'blessed little angel,' who knows it and is lovingly called that every day of his life. Even the thought that anyone would refer to Trig by any disparaging name is sickening and sad.
"CBS should be ashamed for continually providing a forum to propagate lies. Consider the source of the most recent attention-getting lies -- those who would sell their body for money reflect a desperate need for attention and are likely to say and do anything for even more attention."
In the Rodriguez interview, Johnston also discusses an upcoming photo shoot in Playgirl magazine, saying it will be done tastefully.
"The Early Show" has invited Sarah Palin to appear on the show more than a dozen times. She has declined.
In Part Two of the interview, Johnston tells Rodriguez he knew Palin would quit as governor as soon as she began fielding many big-money offers to do other things. He also spoke more about the Playgirl spread, and addressed the chances of a reconciliation with the Palins:
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