A Yale Law Journal article offers illuminating commentary on the nature and scope of high crimes and misdemeanors:
Indeed, in subsequent remarks on September 8, Madison indicated specifically that the power of the House to impeach extended to “any act which might be called a misdemesnor,” a criterion much different from “high crimes and misdemeanors against the State. Thus, although several recent commentators have concluded from the exchange of September 8 that the Convention rejected “maladministration” as a standard for impeachment, it is more accurate to say that the Convention accepted “high crimes and misdemeanors against the State” as a standard for mandatory removal, after one delegate-Madison-had questioned “maladministration” for such a purpose.
One need only consider later assertions by Madison himself to confirm that the effect of Article II, section 4, is neither to confine impeachable offenses to “high crimes and misdemeanors” nor to reject “maladministration” as a ground for impeachment. Speaking before the Virginia ratifying convention Madison suggested that “if the President be connected in any suspicious manner, with any person, and there be grounds to believe he will shelter them, the House of Representatives can impeach him; they can remove him if found guilty.” He later indicated that the President was impeachable for “abuse of power.”
Impeachment power can be interpreted to be quite expansive. The article continues:
Other public comment and actual practice in the period immediately following the drafting of the Constitution indicate that impeachment was understood in the light of earlier English and American practice, and that impeachable offenses were not generally seen as limited to “high crimes and misdemeanors against the State.” A theme which runs through the state ratification debates is that impeachment serves to make public officials “answerable” to the people. Impeachable conduct included: conduct exciting suspicion; “malconduct” and abuse of power; making bad treaties (James Wilson); an attempt by the President to push a treaty through the Senate without a quorum being present (John Rutledge); behaving amiss, or betraying public trust (Charles Pinckney); “any misdemeanor in office” by the President, and giving false information to the Senate (James Iredell); abuse of trust “in any manner” by the President (Richard Spaight); “any maladministration in his office” by the President; and misbehavior (Governor Randolph of Virginia). Moreover, in the debates of the First Congress on the Executive Departments, the standards proposed for impeachment of the President included “maladministration, “misdemeanors,” “malconduct,”; misbehavior, “displacing a worthy and able man,” indolence and infirmity. John Vining, of Delaware concluded that the people have the means of “calling [the President] to account for neglect.”” Finally, in the trial of Judge John Pickering in 1803, the Congress impeached and convicted a federal judge for drunkenness. The crucial feature of the Pickering case is that the Senate appears to have consciously rejected “high crimes and misdemeanors” as the necessary standard for impeachment and removal.
The president can exercise the pardon power but Congress can punish the president by impeachment. Trump supporters take refuge in the plenary interpretation of the pardon power, but their arguments against impeachment has little merit.