Actually, George Washington didn't establish a 2 term limit. He only served for 2 terms because he felt it was not right for a newly formed Republic which broke free from a Monarchic Tyrant to have a leader for more than a couple of years. I'm sure his own fatigue was a major factor in leaving after two terms, but Washington did not wish to serve for more than 8 years. He hoped future presidents would follow that ideal, and some did, others (such as FDR) obviously didn't.

Since George Washington didn't establish a 2 term limit I will try to answer what would I think would happen if in 1951 the 22nd Amendment wasn't passed.

The only President that may have won a 3rd Term Limit after FDR would have been Dwight Eisenhower. He was an effective and strong President and if there wasn't an Amendment preventing three terms he may have won. Whether he would have run is something only an expert on Eisenhower could answer. I doubt it, but I think he would've won.

Lyndon Johnson is an if, he may have won but probably not. There is not other president that would've won a third term except Eisenhower, in my opinion.

I honestly can't think of what would've happened to Presidents effectiveness or urgency in office, but I don't think it would have changed much considering they still had to win elections.

So to sum up, Washington didn't establish a term limit, one was established in 1953, and the only thing I think that would've been severely different is Eisenhower possibly running for more terms. How that would've turned out, I have no clue.

I hope I've been helpful.