I don't know very much about Harry Truman. Did he have a problem with an executive order?
Yes, Truman tried to nationalize all steel mills in the country with an Executive Order. For the first time in history - although, up until that point, EO's hadn't really been used in quite that way - the Supreme Court granted cert on such a challenge to Executive authority on EOs The case was Youngstown Sheet & Tube Co. v. Sawyer. The Supremes held for the plaintiff, ruling Truman's EO unconstitutional.
That set the guidelines that are in place today - Executive Orders can't undo enacted legislation, or violate the Constitution.