The claim is false.
I'm going to quibble with the phrasing and be really strict since the framing is manipulative/dishonest.
Has any president wanted a raise in the minimum wage but been denied it by the opposing party?
The minimum wage goes back to 1938 but I can't find good records online of things proposed to the house/senate before the late 1980's.
I'm not excluding when they wanted a raise at some point, were denied and later got some kind of a minimum wage increase during their term. If there was any kind of "no" to any minimum wage increase during their term I'm counting it.
During most of Clintons term 1993-2001 the republicans controlled the house and the senate from 1994 until the end of his term. So we can accept any proposed minimum wage increases that didn't happen in that term.
Clinton was pro-increase. So proposals during his term count.
Here are the increases that did happen:
Note that what actually happened was that in 1995 the minimum wage was $4.25 , in 1996 the minimum wage was $4.75 and in 1997 the minimum was $5.15.
January 11 (legislative day, JANUARY 10), 1995 the American Family Fair Minimum Wage Act of 1995 was Introduced in Senate.
It proposed that in 1995 the minimum wage would be set at $4.75 and $5.25 in 1996 and $5.75 in 1997.
This did not happen.
SEC. 2. MINIMUM WAGE INCREASE.
Paragraph (1) of section 6(a) of the Fair Labor Standards Act of 1938 (29 U.S.C. 206(a)(1)) is amended to read as follows:
`(1) except as otherwise provided in this section not less than--
`(A) $4.25 an hour during the period ending on August 31, 1995;
`(B) $4.75 an hour during the year beginning on September 1, 1995;
`(C) $5.25 an hour during the year beginning September 1, 1996; and
`(D) $5.75 an hour during the year beginning September 1, 1997;'.
Note that this is not listed as passed in the senate.
Thus a president, Bill Clinton wanted a raise in the minimum wage but the proposed raise was denied by the opposing party at the time, the republicans who controlled the house and the senate.
Later a different raise for a different amount in a different year did go through.
The claim is false.