Shrum recalled one of Kennedy's last hurrahs, saying it was difficult for Kennedy to leave the hospital and go to the Democratic National Convention last year. Shrum said he prepared brief remarks for the ailing Kennedy to deliver, but Kennedy rejected them.
"I'm not coming to the Democratic convention to speak for 30 seconds," Kennedy growled.
Shrum said that more than 2,500 pieces of legislation have Kennedy's name on them, and more than 300 became law.
"He really accomplished more than many presidents do," he said.
Shrum Kennedy's determination to fight for health care reform even while dying was typical.
"He could weigh in on the phone… he was talking to the president," he told "GMA." "It was the cause of his life and he fought it all the way to the end of his life."
"His basic instruction was to keep pushing forward…I think he believed and we believe that there's forward momentum here," Obama's senior adviser David Axelrod told "GMA."
Even political foes praised Kennedy. Former president George H.W. Bush, a Republican, issued a statement calling Kennedy a "seminal figure" and offered his condolences on behalf of himself and his wife Barbara.
"While we didn't see eye-to-eye on many political issues through the years, I always respected his steadfast public service," Bush said.
Calling him by the family nickname "Teddy," California Gov. Arnold Schwarzenegger, a Republican who is married to Kennedy's niece Maria Shriver, lauded Kennedy's work on health care.
"Teddy taught us all that public service isn't a hobby or even an occupation, but a way of life, and his legacy will live on," Schwarzenegger said.
Nancy Regan, wife of former President Ronald Regan, said the two men respected each other despite their divergent political views.
"Ronnie and Ted could always find common ground, and they had great respect for one another. In recent years, Ted and I found our common ground in stem cell research, and I considered him an ally and a dear friend," Regan said in a statement.
Kennedy's life began as one of nine children of Joe and Rose Kennedy, who groomed their children for public service, even the presidency. His mother's famous motto was, "To whom much is given, much is expected."
It took a while for Ted Kennedy, the youngest of the famous brothers, to live up to that standard. He was kicked out of Harvard College for cheating, though he was later readmitted and graduated. It was the first of several incidents that tarnished Kennedy's early reputation.
He was elected to the Senate in 1962, taking over the Massachussets seat after his brother John became president. He survived a plane crash that broke his back, endured the assassinations of his brothers, and bore the mantle of the family's last hope for a presidential dynasty.
Those hopes were dashed in 1969, however, when Kennedy veered off a bridge in Chappaquiddick, killing young Kennedy volunteer Mary Jo Kopechne. Kennedy's failure to save her or report her death for 10 hours haunted his career and was considered partly to blame for his failure to wrest the Democratic nomination from President Jimmy Carter in 1980, his last attempt to win the presidency.