Who said of his decision to become Vice President of the U.S. that it was the "worst damn fool mistake I ever made"?

The same one who said the position was "not worth a bucket of warm piss" John Nance Garner

You got it, Georgia! John Nance Garner, the first of FDR's three veeps, gave up the position of Speaker of the House to become V.P. His quote is usually rendered ad "a warm bucket of spit: but yours is much more likely to be true.

And interestingly enough he ran against Roosevelt in the Democratic Primary! Perhaps to see if being a president was better than being a vice-president?

I think in most of the primary races in the last 2/3 of the 20th Century, at least one VP candidate was originally an opponent of the man he later shared a ticket with. LBJ was a close opponent of JFK in the Primaries, and everybody was an opponent of Nixon's in the 60 race. In 64, several were opposing Goldwater for the Republican slot, and Miller may have been one. In 68, had Robert Kennedy not been assassinated, either he or Humphrey would have been the VP with the other in the Presidency. The 72 Democratic primaries were a free for all, and in 76, Carter and Mondale were opponents. In 1980, future VP Bush called Reagan's economic ideas "Voodoo Economics" yet ended up taking the bottom half of the ticket to the Voodoo Master. In 92, Gore was Clinton's primary opponent. I am also sure I have forgotten a few who ened up on the bottom half of a ticket they wanted to head.