In Nixon's first book, published in 1962, he discusses six of his major political crises. One of these was, of course, the Checkers Speech. The section on the speech is basically a defense of the whole affair—after all, it's his book. Even so, it's difficult to be too hard on the guy: he was falsely accused (this time at least).
The Checkers Speech is included in Safire's book as a term for any speech made by a politician which is emotionally over-charged. It's an idiom that's lost traction for most people, but it's still prevalent in the political science community.
That's right: the speech was so over-the-top that they named every other schmaltzy speech after it.
One of the inspirations for Nixon's Checkers story was a speech by FDR, made on the exact same day eight years earlier. FDR was responding to a smear by Republicans that he'd accidentally left his little Scottish terrier Fala behind on an island while touring the Pacific, and had sent a Naval Destroyer back to retrieve her. FDR turned the scandal into a joke, deftly deflecting the controversy. Nixon used a similar dog-friendly strategy, though in his case it was more opportunistic; nobody had heard of Checkers before the speech.
The 2004 U.S. Presidential election wasn't all that different from the 1952 election: you had a Democratic candidate who was seen as something of an aristocratic egghead (John Kerry), and on the Republican ticket you had the extremely likeable George W. Bush. Bush was famously declared "the candidate you'd rather have a beer with" in a Zogby/Williams poll.
This personable image was an important factor in Bush's victory over Kerry, despite a lot of controversy because of messy foreign wars, 9/11, deregulation, and a mini-recession that occurred during his first term. It was this same likeability factor that Nixon was going for in his Checkers Speech.
Spitzer was a powerful politician in New York politics who had risen as the Attorney General and eventual Governor of New York in 2006. Two years later, it was revealed that Spitzer had been deeply involved with a high-end prostitution ring. It threatened to end his political career.
Spitzer tried to get ahead of the scandal, ordering a press conference to respond. Rather than an open and honest approach, Spitzer vaguely referred to this as a "personal matter," and ended the press conference without taking questions. He'd later be called upon to resign, and during his resignation speech there were certainly flashes of the Checkers Speech pathos. Spitzer slowly tried to get back into the political game, but with less success than Nixon had.
President Clinton called a press conference after rumors were made public about an affair with Monica Lewinsky, a young intern at the White House. By taking to the airwaves, he hoped to speak directly to the people and put the scandal behind him. He took a page from the Nixon playbook, looking us straight in the eye and saying, "But I just want to say one thing to the American people. I want you to listen to me. I'm going to say this again. I did not have sexual relations with that woman, Miss Lewinsky. I never told anyone to lie, not a single time, ever."
Clinton had one problem Nixon didn't have, though.
He was lying.
He did have sexual relations with that woman. Seven months later, he was back on TV again, this time in a speech devoted entirely to the scandal. He even looked as somber as Nixon after Watergate as he admitted having the sexual affair and lying to the American people about it. Like Nixon, he thought that this prying into his personal life was part of a larger politically-motivated attack that had been going on for years.