Claremont, Calif. — What kind of conservative is President Trump? He must be some kind of conservative, because for nearly 100 days and counting, liberals have poured on him the kind of vitriol they do not reserve for moderates or ideological nobodys. Inside the Beltway, some famous conservatives have joined in the sport but for the opposite reason, that Mr. Trump, they claim, is no conservative but a populist demagogue out to discredit and destroy their beloved movement.

In his three major public speeches so far — his remarks at the Republican National Convention, his Inaugural Address and his speech to a joint session of Congress — Mr. Trump did not mention conservatism at all. Even at the Conservative Political Action Conference, he claimed simply, and almost in passing, that his election was a victory for “conservative values.” What those were he did not specify, except to say that Americans believe in “freedom, security and the rule of law” and in standing up for America, American workers and the American flag.

These formulas are sufficiently broad to encourage both sides of the White House jostling between Stephen Bannon, the chief strategist, and Jared Kushner, Mr. Trump’s son-in-law. Rather than focus on the infighting, we need to look at the president’s overall agenda and try to put it into a longer, and sharper, historical perspective. Granted, there has never been a president quite like Mr. Trump, but his positions are not as outré or as outrageous as they are often portrayed.

Mr. Trump remains the kind of conservative president whom one expects to say, proudly and often, “the chief business of the American people is business.” Although Calvin Coolidge said it first, Mr. Trump shows increasing signs of thinking along broadly Coolidgean lines, and of redirecting Republican policies toward the pre-New Deal, pre-Cold War party of William McKinley and Coolidge, with its roots in the party of Abraham Lincoln.