"I just hope they understand that Tony was loved here in the White House," Bush said.
"I've known or worked with a lot of press secretaries, White House press secretaries, in my 40 years in Washington, and I'd have to say that Tony's the best," Cheney said on "FOX News Sunday," the show first hosted by Snow.
"He had this rare combination of intelligence, of commitment and loyalty to the president that he was working for, but also this great love of going out behind that podium and doing battle with what in effect were his former colleagues. And it was this capacity that he had to be unfailingly polite, to maintain good humor under the most trying of circumstances, and do it, I thought, better and more effectively than anybody I've ever seen in that post," Cheney said.
Snow died at 2 a.m. Saturday at Georgetown University Hospital in Washington, D.C.
"Laura and I are deeply saddened by the death of our dear friend Tony Snow," President Bush said in a written statement. "The Snow family has lost a beloved husband and father. And America has lost a devoted public servant and a man of character."
"It's a tremendous loss for us who knew him, but it's also a loss for the country," Roger Ailes, chairman of FOX News, said Saturday morning about Snow, calling him a "renaissance man."
Snow, besides being the original anchor of "FOX News Sunday" in 1996, hosting each week from historic homes in Washington, D.C., because the burgeoning network had no studio, he also hosted FOX News' "Weekend Live" and a radio program, "The Tony Snow Show," before departing for the White House in 2006.
As a TV pundit and commentator for FOX News, Snow often was critical of Bush before he became the president's third press secretary, following Ari Fleischer and Scott McClellan. He was an instant study in the job, mastering the position — and the White House press corps — with apparent ease.
"One of the reasons I took this job is not only to work with the president, but, believe it or not, to work with all of you," Snow told reporters when he stepped into the post in 2006. "These are times that are going to be very challenging."
During a tenure marked by friendly jousting with journalists, Snow often danced around the press corps, occasionally correcting their grammar and speech even as he responded to their questions.
"He would unfailingly challenge the premise of many of the questions. I'd never seen this before in a press secretary," said conservative radio host Rush Limbaugh. "He challenged the premise and told them that they were wrong in the narrative or the storyline that they were tacking, and this caused the president's supporters, those who had seen it, to stand up and cheer."
"Tony did his job with more flair than almost any press secretary before him," said William McGurn, Bush's former chief speechwriter. "He loved the give-and-take. But that was possible only because Tony was a man of substance who had real beliefs and principles that he was more than able to defend."
As he announced Snow as his new press secretary in May 2006, Bush praised him as "a man of courage [and] a man of integrity." Snow presided over some of the toughest fights of Bush's presidency, defending the administration during the Iraq war and the CIA leak investigation.
"I felt comfortable enough to interrupt him when he was BSing, and he kind of knew it, and he'd shut up and move on," Snow said.
His tenure at the White House lasted 17 months and was interrupted by his second bout with cancer.
Snow had his colon removed and underwent six months of chemotherapy after he was diagnosed with colon cancer in 2005. In 2007 he announced his cancer had recurred and spread to his liver, and he had a malignant growth removed from his abdominal area.
He resigned from the White House six months later, in September 2007, citing not his health but a need to earn more than the $168,000 a year he was paid in the government post. He was replaced by his deputy, Dana Perino, Bush's current press secretary.
After taking time off to recuperate, Snow joined CNN as a political commentator early this year.
At the White House, Snow brought partisan zeal and the skills of a seasoned performer to the task of explaining and defending the president's policies. During daily briefings he challenged reporters, scolded them and questioned their motives as if he were starring in a TV show broadcast live from the West Wing.
"The White House has lost a great friend and a great colleague," said Perino in a statement released to the media. "We all loved watching him at the podium, but most of all we learned how to love our families and treat each other."
Critics suggested Snow was turning the traditionally informational daily briefing into a personality-driven media event short on facts and long on confrontation. He was the first press secretary, by his own accounting, to travel the country raising money for Republican candidates.
As a commentator, he had not always been on the president's side. He once called Bush "something of an embarrassment" in conservative circles and criticized what he called Bush's "lackluster" domestic policy.
A sometime fill-in host for Rush Limbaugh, Snow said he loved the intimacy of his radio audience.
"I don't think you ever arrive," he said. "I think anybody who thinks they've arrived or made it, anywhere in the media — they're nuts."
Robert Anthony Snow was born June 1, 1955, in Berea, Ky., the son of a teacher and nurse. He graduated from Davidson College in 1977 with a bachelor's degree in philosophy, and he taught briefly in Kenya before embarking on his journalism career.
Because of his love for writing, Snow took a job as an editorial writer for the Greensboro Record in North Carolina and went on to run the editorial pages at the Newport News (Virginia) Daily Press, Detroit News and Washington Times. He became a nationally syndicated columnist, and in 1991 he became director of speechwriting for President George H.W. Bush.
"He served people, and we can learn from that. He was kind, and we can learn from that. He was just a good person," the senior Bush told FOX News.
Snow played six instruments — saxophone, trombone, flute, piccolo, accordion and guitar — and was in a D.C. cover band called Beats Workin'. He also was a film buff.
"He was a great musician," Ailes said. "And he loved movies."
More than anything, said Snow's colleagues, he was a joy to work with.
"He was a lot of fun," his former FOX News producer Griff Jenkins said. "This is a loss of a family member."
FOX News Chief Washington Correspondent Jim Angle called Snow a "gentleman."
Snow is survived by his wife, Jill Ellen Walker, whom he married in 1987; their son, Robbie; and daughters, Kendall and Kristi.
The Associated Press contributed to this report.
We offer our deepest sympathies to Tony Snow's family, friends and co-workers. He will be greatly missed. ~ Sparky