There is a good link on the Senate dealing with the vote count situation, here. It was an off-year election, after Nixon's situation had blossomed to full bloom, not being a crook and all. It is coincidence, we have one going out, not being a dunce, allegedly.
Wikipedia discusses and links to Chief Justice Warren's opinion, Powell v. McCormack, 395 U.S. 486 (1969), which was an ethics challenge to seating a House member, not a vote count challenge.
Coleman appears to have each dimension in his closet, too few votes, and Nasser's suits.