The US was NOT a great nation in 1935, before the 50's the only way/time America was "great" was during the "guilded age" or the "roaring 20s" when inequality was astronomical and the US was ran by aristocracy and corruption was even more widespread than it is today. It was GREAT for rich white people, it SUCKED royal ass for everyone else. The labor class worked horrid conditions or very very very little pay, quality of life was low, life expectancy was low, poverty was rampant.
America became great during the "Golden Age of Capitalism"(the 50's - 70's), ironically when Unionization rates were over 70% and as unionization has dropped so has wages for the middle class.
And yes, the the 40' 50's and 60's are DEFINITELY what made America what it was....the New Deal... Eisenhower and his IS system(and other public works projects...the Great Society...these things are absolutely what made us that great nation we became. The Golden Age of Capitalism.....it was conservatives who destroyed this nation, started with Nixon, came unto it's own under Reagan, and Bush II finished the job. We are back to where we were in the 20's, an economy based on legalized gambling(finance), unbelievably high inequality, and an elite class who live like gods. Nowadays the only way conservatives can still claim that anyone can obtain the "American Dream" are BECAUSE of the public systems which provide assistance to the poor that have survived, once they are gone(and it won't be too long) if you don't got money, you ain't getting any.
Oh, and let's not forget the CIVIL RIGHTS MOVEMENT, I don't see how you can possibly say America was "great" before the Civil Rights movement.