The last POTUS to have a "real job" would have been Harry S. Truman. Truman had been a farmer (and spent plenty of time looking at the backside of a mule while working the land), then opened a habadashery (at which he was pretty much a failure). I would say that Truman was the last "real American" to hold the office, as he had served in the Army at a young age, then come out into the private sector, worked and struggled in the private sector before going into politics. Truman got to the presidency completely by accident: FDR chose him for the VP slot purely because Truman was seen as a "bumpkin" from the sticks, who wouldn't rock the boat much in DC. FDR figured he would complete his fourth term and Truman would have been none the wiser. Truman didn't so much achieve the presidency as had it dumped on him in a time of crisis. 

If you read the press accounts at the time, no one in DC was happy with Truman. He was excoriated constantly in the press, seen as a simpleton, a man who didn't see all the "nuance" and "skill" that should be applied to various positions. Truman, for his part, told people where to shove such nonsense. The more I read of Harry Truman, the more I like the man's style. In hindsight, we were fortunate and lucky to have a POTUS like Truman, a man who could make decisions quickly based on his own bedrock principles.

Eisenhower we can give a pass to, since he was a professional military man, and that indeed real career path. Ike was fortunate in that America was in the midst of a secular economic boom following WWII, because the failing of military men is that they don't know much about the private sector economy.

From JFK onwards, however, we've been in a downward spiral as the press has effectively created a requirement that all candidates have political experience, rather than private sector experience, to hold office. LBJ accelerated the downward spiral faster than any man who held the office until about now.