The jesting offer came when writer Nora Ephron said Streep's talent, versatility and resemblance to Clinton made it "inevitable" that she would one day play the secretary of state and former first lady. Clinton, who flew home for 36 hours to celebrate the honorees over the weekend, just laughed, while Streep jokingly stood up for a better look at the nation's top diplomat.
Along with Streep, pop singer Neil Diamond, Broadway singer Barbara Cook famed cellist Yo-Yo Ma and jazz saxophonist Sonny Rollins joined in receiving the nation's top award Sunday night for those who have influenced American culture through the arts.
Caroline Kennedy, who hosts the show as part of a living memorial to her father, John F. Kennedy, acknowledged her personal connection to one honoree.
In a nod to Diamond, she said he was "a Brooklyn lad with a gift of melody who grew into a solitary man, `reaching out, touching me."' That was enough to draw big laughs as the crowd of celebrities and politicians recalled that Diamond's "Sweet Caroline" was named for her.
"I'm going to have to thank her for that," Diamond said before the show, noting that the song is a story about him and his former wife. But he took the name from Kennedy.
Smokey Robinson sang "Sweet Caroline" with help from Kennedy and fans brought in from Boston's Fenway Park where it's a favorite anthem.
Lionel Richie, who sang, "I am... I said," told The Associated Press he got into the music business because he wanted to be Diamond.
"He's a great storyteller," Richie said. "He's not an acrobatic singer. Basically he told the story in a very simple voice."
Classical music stole the show's finale, though, with surprise tributes from Stephen Colbert - who seemed lost at first - and the puppet Elmo from TV's "Sesame Street."
"Tonight we celebrate the greatest living cellist," Colbert said "We chell-ebrate, if you will."
Ma, one of the best-known classical musicians, has played cello since he was 4. At age 7, he played for presidents Kennedy and Dwight D. Eisenhower.
Now at 56, he is hailed as a musical ambassador to the world who has spanned styles from Bluegrass to sounds from the Silk Road with an ensemble he founded. Many of his friends performed in his honor.
Elmo, dressed in a tux, said he came to honor his friend, Ma who taught him that "music is like a playground" that makes everybody happy.
James Taylor and conductor John Williams joined in a performance of "Here Comes the Sun" with a string ensemble.
CBS will broadcast the show on Dec. 27.
Earlier President Barack Obama lauded the actors and musicians at the White House.
"They have different talents, and they've traveled different paths," Obama said. "And yet they belong here together because each of tonight's honorees has felt the need to express themselves and share that expression with the world."
He said everyone has that desire for self-expression in common.
"That's why we dance, even if, as Michelle says, I look silly doing it," he added to laughter.
Secretary of State Hillary Rodham Clinton flew home between visits to Myanmar and Germany to honor the artists with a dinner Saturday night. After visiting the isolated Southeast Asian country also known as Burma, Clinton said such U.S. artists have worldwide influence by using their freedom of creativity.
"You may not know it, but somewhere in a little tiny room in Burma or even in North Korea, someone is desperately trying to hear you or to see you, to experience you," Clinton said. "And if they are lucky enough to make that connection, it can literally change lives and countries."
Streep, 62, has made more than 45 movies and won two Oscars in her career. Her movies have spanned Shakespeare and "Angels in America" to portraying chef Julia Child in "Julie and Julia."
In her upcoming film, Streep will play British Prime Minister Margaret Thatcher in the upcoming "The Iron Lady."
Streep said she was in awe of the accolades from the president and others.
"Look where we are, look who's here," Streep told The Associated Press. "It's overwhelming. I feel very proud."
Emily Blunt and Anne Hathaway who co-stared with Streep in "The Devil Wears Prada," joined Kevin Kline and Stanley Tucci for a musical tribute to Streep.
Sarah Jessica Parker and Matthew Broderick opened the tributes to Cook, recalling the days when they first started dating and went to hear Cook sing at the CafDe Carlyle in New York.
"I don't think Matthew at the time knew what kind of special memory he was creating for us," Parker said.
"Oh, I knew," Broderick said back.
Cook, 84, made her Broadway debut in 1951, and later Leonard Bernstein cast her in his musical "Candide." She topped that performance as Marian the Librarian in 1957's hit musical "The Music Man," for which she won a Tony Award.
A film tribute noted Cook went silent for a decade, due to drinking and depression, but she came back.
Glenn Close called her an icon for anyone who has worked on Broadway.
"I think we have the biggest respect for her because she really has survived, survived and prevailed," Close said.
Rollins, 81, is a jazz saxophonist who has shared the stage with Miles Davis and Dizzy Gillespie, among others.
"America is the home of jazz. It's what we started," he said. "By the way, hip hop music is a part of jazz, believe it or not."
Friend Bill Cosby marveled about how he has heard Rollins' distinctive sax around the world in Greece, Hong Kong, Italy - and found so many people who knew the musician's work.
"All over the world, Sonny Rollins," Cosby said.
Benny Golson and Herbie Hancock joined in playing some of Rollins' tunes.
Fellow sax player and former President Bill Clinton said earlier that he has been a fan since the age of 15 or 16 when he bought his first Rollins LP and played it until it was worn out.
"His music can bend your mind, it can break your heart, and it can make you laugh out loud," Clinton said. "He has done things with improvisation that really no one has ever done."
Associated Press writer Alan Fram contributed to this report.