Douglas Kmiec, former head of the DoJ OLC under Reagan and Bush 41, gives a definitely maybe to the idea of a successful subpoena against Trump:
In 1988, with a White House entangled by Iran-contra, the O.L.C. was asked whether a president could be ordered to comply with a criminal subpoena seeking his testimony. We also responded in the negative — but it was not a simple, categorical no. The presidential subpoena is a valid legal tool, as Chief Justice Warren Burger made clear in United States v. Nixon, but a president may find case-specific reasons to resist it.
Recall that Richard Nixon had to give up his tapes — but the narrow ruling regarded pre-existing documents (as opposed to testimony), and the president himself was not the criminal defendant. The Supreme Court explicitly noted the absence of “a claim of need to protect military, diplomatic or sensitive national security secrets.” Watergate history affirms the common-law maxim that the law is entitled to every person’s evidence, but the court is sensitive to both interference with presidential responsibility and refusals for information anchored within executive privilege or the protection of open investigations.
About the only thing one can say for sure about the enforceability of a presidential subpoena is that, should the Trump and Mueller sides fail to agree on a setting for presidential interview, both sides have a basis to litigate the matter tenaciously.
The subpoena outcome is necessarily informed by highly contextualized facts.
And since we don't know the full set of facts behind a possible Mueller subpoena of Trump it is hard to say in advance what the court would do.
I would welcome some legal advice on this passage, from the intro:
The letter [From Trump's legal team to the DoJ] is more monarchal than respectful of the separation of powers and our democracy’s constitutional checks and balances. Its claims that the president can “order the termination of an investigation by the Justice Department or F.B.I. at any time and for any reason” is unprecedented and far exceeds even Harry Truman’s brazen and rejected attempt to take over the steel mills to blunt labor unrest in the 1950s.
Say what? I would have thought the President's control of the Executive Branch was far stronger than his control of external unions and industries, regardless of Truman's national security arguments.
Then again, my recollection from Nixon's Saturday Night Massacre is that the President can not give orders to the underlings in the DoJ. Nixon wanted to fire Special Prosecutor Archibald Cox but could not do so directly. Therefore he kept firing Attoneys General until he found one willing to do the deed.
Of course, Archibald Cox's Special Prosecutor office was a legislative creation that differs from Mueller's Special Counsel status. Congress has mooted legislation specifically protecting Mueller but has not passed it. On the other hand, I believe I have read that there is chain-of-command legislation governing the DoJ, the upshot of which is that Trump can fire the AG but not any of the underlings. If I am right about that than the President can not directly, e.g., order the halt of an FBI investigation; he would need to find a cooperative AG.
So, my question - is that the sort of objection Kmiec has in mind - that a Trump order to the head of the FBI to halt an investigation would specifically exceed a statutory limit in a way that attempting to nationalize the steel industry would not? I'm baffled.