Naturally, he had little good to say about US presidents and the presidency, though in one of the following quotes there's a hint of liking for Calvin Coolidge, if only by comparison with his predecessors and successors. So without further ado, some Mencken quotes on presidents and, lastly, the office itself:
"[T]he only thing wrong with Abraham Lincoln's Gettysburg Address was that it was the South, not the North, that was fighting for a government of the people, by the people and for the people."
"[Warren Harding's] speeches left the impression of an army of pompous phrases moving over the landscape in search of an idea; sometimes these meandering words would actually capture a straggling thought and bear it triumphantly a prisoner in their midst, until it died of servitude and overwork."
"[Warren Harding] writes the worst English I have ever encountered. It reminds me of a string of wet sponges; it reminds me of tattered washing on the line; it reminds me of stale bean-soup, of college yells, of dogs barking idiotically through endless nights."
"We suffer most not when the White House is a peaceful dormitory, but when it is a jitney Mars Hill, with a tin-pot Paul bawling from the roof. Discounting Harding as a cipher, Coolidge was preceded by one World Saver and followed by two more. What enlightened American, having to choose between any of them and another Coolidge, would hesitate for an instant?"
If there had been any formidable body of cannibals in the country he would have promised them with free missionaries, fattened at the taxpayer's expense." (On Harry Truman's 1948 presidential campaign.)
"The larger the mob, the harder the test. In small areas, before small electorates, a first-rate man occasionally fights his way through, carrying even the mob with him by force of his personality. But when the field is nationwide, and the fight must be waged chiefly at second and third hand, and the force of personality cannot so readily make itself felt, then all the odds are on the man who is, intrinsically, the most devious and mediocre -- the man who can most easily adeptly disperse the notion that his mind is a virtual vacuum.
"The Presidency tends, year by year, to go to such men. As democracy is perfected, the office represents, more and more closely, the inner soul of the people. We move toward a lofty ideal. On some great and glorious day the plain folks of the land will reach their heart's desire at last, and the White House will be adorned by a downright moron."