Snopes confirms that Mencken did make such a pronouncement in 1920 (using the term "downright moron").
In this case the attribution to Henry Louis Mencken, a prominent newspaperman and political commentator during the first half of theMencken biography.
20th century, is accurate. Writing for the Baltimore Evening Sun on 26 July1920, in an article entitled “Bayard vs. Lionheart” (and reprinted in the book On Politics: A Carnival of Buncombe), Mencken cynically opined on the difficulties of good men reaching national office when the scale of their campaigns precluded them from directly reaching out to large segments of the voting public:
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.