He scoured Democracy in America, but could not find the passage. The professor looked, too - and it was not there. The book quoted the last two lines of the passage as coming from Democracy in America but supplied no documentation. The full version of the quotation appeared 11 years later, in an Eisenhower campaign speech. One may conjecture that Eisenhower's speechwriter embellished the lines from the 1941 book and avoided a direct reference to Tocqueville as a way of covering himself.
Speechwriters do such things from time to time.
In his wonderful primer on politics, Playing to Win, Jeff Greenfield presented a model stump speech complete with a fake quotation from the Greek philosopher Heraclitus. Whatever its origin, the passage found its way into circulation. President Reagan used it in a 1982 speech, though his speechwriter hedged by attributing it to Eisenhower's quotation of Tocqueville. Thereafter, his speechwriters grew less careful, and several subsequent Reagan addresses quoted from the passage without any qualifications. At this point, it started showing up with greater frequency in political rhetoric.