The Dolphins did not visit the White House in 1972 because then-President Richard Nixon was involved in the Watergate scandal.
Letterman said that Nixon was also a Washington Redskins fan and did not want to support another NFL team with a White House invitation.
"So they've been sitting around, year after year, wondering, waiting and not getting a call," Letterman said. "They were thinking, 'Well, it might be nice to go to the White House.' "
"Just ask Hillary Clinton what that's like," Letterman added.