Later he adds: “There are an awful lot of people who are looking for a voice that represents the people who feel disaffected.” And: “I do want to be more of a voice of reason and moderation in the Republican Party.”

Hogan is attracting notice partly because he just romped to re-election over the progressive Democrat Ben Jealous — becoming the first G.O.P. governor to win re-election in Maryland since 1954 — and partly because he’s one of only three Republican governors in deep-blue states (Massachusetts’s Charlie Baker and Vermont’s Phil Scott are the other two). His approval rating is 68 percent in a state where Democrats outnumber Republicans 2 to 1.

But mostly Hogan makes no secret of his disdain for the president, though he goes out of his way to avoid mentioning his name. In his second inaugural address this week (written with the help of Mark Salter, John McCain’s old wordsmith), he merely noted that his father, the late Congressman Lawrence Hogan, was “the first Republican to come out for the impeachment of President Richard Nixon.”

“Despite tremendous political pressure,” Hogan said of his dad, “he put aside partisanship and answered the demands of his conscience to do what he thought was the right thing for the nation that he loved.”

That doesn’t quite answer the question of whether Hogan would really contemplate a run — though he is traveling to Iowa in March, ostensibly in his role as vice chairman of the National Governors Association. The downside of any primary challenge is that it is guaranteed to be nasty: Nobody emerges from an encounter with Trump without feeling soiled. It’s also likely to be losing: With the qualified exception of Lyndon Johnson in 1968, no incumbent president who sought his party’s nomination has failed to win it since Chester A. Arthur in 1884.