Ex Parte Garland, decided by the U.S. Supreme Court back in the Reconstruction Era, lays out a pretty much unlimited pardon power, except for cases of impeachment. That aligns with the text of the Constitution in Article II, Section 2, which only mentions impeachment as an unpardonable conviction.
I'm not certain if the original Hamiltonian justification for a full pardon power is necessary any longer. For example, I think amending the Constitution to bar a president from pardoning someone convicted of Treason under the difficult standard outlined explicitly in Article III of the Constitution would not be entirely unreasonable.
It's certainly worth discussing - especially in an era when the Executive's power in this area has much more potential heft, as he maintains an entire office devoted to poring over applications for pardon and other forms of clemency. (Interestingly, though, the total number of pardons granted per President has generally decreased since Truman, with Clinton as an anomaly).