"He was in good spirits, cracking jokes. His nurses, some of them are new, they don't really know him, so they don't understand that sarcasm is his form of affection," Salter said Monday on "CBS This Morning." He visited with the senator about a week ago.
Salter served on McCain's staff for 18 years, including as chief of staff, and has written seven books with him. "The Restless Wave," published by Simon and Schuster, a division of CBS, goes into more depth about McCain's cancer diagnosis and how he wants to be remembered.
McCain, a celebrated military veteran who was a prisoner of war during the Vietnam War, was born into a military family. His two sons also went on to join the military. But Salter said it's more than the military tradition.
"It's 60 years now of service to this country, in uniform and in public office. That's a long, long time. And it means something very personal to him and he wanted to express gratitude and the joy he's had for being able do that," Salter said.
The book was already in the works when McCain's cancer diagnosis was revealed, but Salter said "it became a different book" thereafter – more personal.
"He said, 'Well, let's write a forward and a conclusion that I can record while I'm still strong enough to do it,' so we did that. And those are probably the most personal parts of the book," Salter said.
While known for his bipartisan approach on Capitol Hill, McCain was also known to fight bitterly when he disagreed with leaders of both parties, including former Presidents George W. Bush and Barack Obama.
"He fights. So he's fought with everybody at one point or another. You know, he always talks about the country being 325 million opinionated, vociferous souls – and he's one of them," Salter said.
"But he recognizes that so much more unites us than divides us, and that in this country the only way you can get things done is together, to make incremental progress in the problems of our time," he added. "That if you just scream and yell and stand for 100 percent of your way, nothing gets done."
On a personal note, Salter said it's been a "great privilege" to collaborate with McCain on his books.
"This is usually John's job. The part I like about ghostwriting is the ghost part," Salter said, as the "CBS This Morning" co-hosts reacted with laughter.
"The Restless Wave" goes on sale Tuesday, May 22.