Schieffer admitted that because he is a "cynical Washington reporter" he came to the interview with a "secret agenda."
After showing a picture of a young Walter Cronkite with puppet Charlemagne the Lion, Schieffer asked Elmo, "could you come and be my co-anchor? I think it would be great for the ratings."
"Only if Mr. Bob comes to Sesame Street too," Elmo slipped in. It was an offer Schieffer could not resist. "It's a deal," he said.
The Sesame Street celebrity was in Washington this week to join the Department of Health and Human Services in teaching school children how to avoid the H1N1 virus, as well as to promote a PBS program which helps children understand how to sacrifice in tough economic times. (The prime time program, "Families Stand Together: Feeling Secure in Tough Times," airs September 9th on PBS.)
Watch the interview above. And click here to watch for the rest of today's show, which includes interviews with former Secretary of Homeland Security Tom Ridge and Politico's Mike Allen. "Washington Unplugged" appears live on CBSNews.com each weekday at 12:30 p.m. ET. Click here to check out previous episodes.