According to the San Francisco Examiner, 19 June 1992, A-1, A-16,
Quayle said

"As Mark Twain once said, 'You should never trust a man who has only one way
to
spell a word.'".  The same article reported that UC-Berkeley scholars
working on his papers couldn't validate the
authenticity of the quote.  The quote was evidently found in at least three
other collections of quotes "who
attributed the remark to Twain without saying when and where or how."

According to the Examiner "In the Bancroft archives only one item comes
remotely
close, Hirst said.  It's a speech Clemens gave in May 1875 after a
fund-raising spelling bee at the First
Congregational Church in Hartford, Conn.
He lost out by dropping the silent 'h" out of 'chaldron,' a term for 36
bushels
of coal.
      "He said:  'I don't see any use in spelling a word right, and never
did.
I mean I don't see any use in having a uniform and arbitrary way of spelling
words.  We might as well make all our
clothes alike and cook all dishes
alike.'

The could be the original source of the Quayle quote, Hirst speculated, if
it had been paraphrased and altered
through retellings over the years."