Appearing on "This Week," ABC News Chief Anchor George Stephanopoulos, who served as a senior adviser in the White House during Ginsburg’s confirmation, asked the former president how Ginsburg's tenure on the court surprised him.
"She was only different as I never anticipated she would become, later in her life, a cultural icon and we'd all be doing her exercise routine," Clinton said of second woman to serve on the United States' highest court.
"The more I think about it, the less surprised I am because in a time where people are so cynical, Ruth Ginsburg symbolizes everything that is best about America and she was always completely on the level," he added. "And she just seemed to be authentic and a person first. And she never disappointed on that."
Stephanopoulos recalled that a key selling point in the former president's nomination of Ginsburg was her ability to maintain cordial relations with conservative judges, like the late-Supreme Court Justice Antonin Scalia.
"The country became more and more polarized, but she maintained her relationships with Justice Scalia and cordiality with the others, even when she was clearly in deep disagreement with them over a variety of cases. And I think that's important. If we quit talking to each other, it's going to be very difficult to ever knit the country back together again," Clinton said.
The sudden Supreme Court vacancy has triggered a political battle to fill Ginsburg's seat in an election year. President Donald Trump told supporters at a campaign rally in Fayetteville, North Carolina, on Saturday that he plans to put forth a female nominee next week.
Senate Majority Leader Mitch McConnell promised a vote on the Senate floor, writing Friday, "Americans reelected our majority in 2016 and expanded it in 2018 because we pledged to work with President Trump and support his agenda, particularly his outstanding appointments to the federal judiciary."
Democrats have slammed the majority leader for his comments, accusing him of "hypocrisy" for blocking a vote on President Barack Obama's nominee to replace Scalia in 2016 during an election year.
"(McConnell) said we had to trust the American people and give the voters a voice in the last Supreme Court selection when President Obama nominated Merrick Garland, 10 months before the election. There has never been a rule on that," Clinton told Stephanopoulos.
"Today it seems that Sen. McConnell has lost his faith in the judgment of the American people and wants to hurry up and put somebody on the court," he added.
With the GOP controlling the Senate 53-47, Democrats must include four Republicans in their coalition to block Trump's nominee.
"(Democrats) should see if anybody cares that several people, including some who are up for re-election are clearly going to violate what they said they believed before. (Sen.) Lindsey Graham has said he wouldn't vote this close to the election no matter what president was there," Clinton said. "Sen. (Chuck) Grassley said the same thing."
Both Graham, the current chairman of the Senate Committee on the Judiciary, and, Grassley who preceded him as chair, have previously expressed opposition to presidents nominating Supreme Court appointments in election years. While Grassley has not said if he plans to support Trump's nominee, Graham tweeted that he would do so.
"It would be very interesting to see whether their position could only be justified as, 'if my party can do it now I'm for it, if their party can do it then I'm against it.' And if that's the rule of life in America, then who knows what the consequences will be" Clinton said.
ABC News' Katherine Faulders and John Santucci contributed to this report.