Let's not kid ourselves: The United States does not truly have a LEFT to RIGHT party mentality. On a global prism, the USA is more like "Center Right" to "Extreme Right". The more 'liberal' party (which I guess would be the Democrats) actually has what the world would view as centrist/moderate views, going more towards right.
Indeed, but there are many reasons why America has been so uniquely conservative among first world nations, and fortunately there are also reasons that this uniformity is changing. I think it's fairly safe to say that in most cases extreme conservatism is a position of fear, you wouldn't want a lot of guns and a huge military unless you (consciously or unconsciously) were very afraid of something. There have been studies supporting this http://abcnews.go.com/blogs/health/2012/09/03/conservatives-and-liberals-have-different-brains-studies-show/ (http://abcnews.go.com/blogs/health/2012/09/03/conservatives-and-liberals-have-different-brains-studies-show/) Very broadly speaking the conservative view is that the world and change is something to be fought against and kept out, while the more progressive one is to embrace progress.
There are many causes of this widespread fearfulness in the US but the single most important one is probably the Cold War. Two entire generations of Americans, first the baby boomers then the generation X'ers, grew up with the constant looming threat of total nuclear annihilation, preparing to fight a third world war that never came.
45 odd years of going to sleep not knowing if you and everyone in your city will be dead before you wake up understandably bred quite a bit of paranoia.
Consequently the cold war period saw a rejection of any ideas that might remotely be considered communist or socialist because of paranoia over possible communist influence or infiltration. The popular term for something or someone who wasn't entirely communist but seemed sympathetic to or reminiscent of ideas from it was "Pinko", not entirely "Red" but close enough. This was probably the start of the fear of "big government" which we still see today.
This era also saw a strengthening of ties of Christianity to the conservative side of government. Initially as a way to distinguish Americans from "godless atheist" communists (this was when "One nation under God" was added to the pledge of allegiance, and when "In God We Trust" was made our official motto) then further when an amalgamation of the historically bickering and backbiting myriad Christian denominations settled their differences to become a political force following the legalization of abortion with Roe. v. Wade in 1973.
Particularly but certainly not only Evangelical preachers steeped themselves deeply into politics, and the hardy fraternity between religious leaders and American conservative talking heads and politicians is held firmly to this day. You can see an example of this in play for the just-passed Presidential election in this humorous montage put together by a prominent atheist on youtube.
NON-STOP TOTAL FAIL!! (http://www.youtube.com/watch?v=c9UQVZvS-IE#ws)
I could go on for a long time about other things, how most Americans are sheltered from the more unpleasant facts of their own history such as the well documented genocide of millions of Native Americans. But those listed above are the main reasons American conservatism flourished in the last century.
In the 20th Century when America still had a vast wealth of natural resources and the benefit of being one of the few first world nations without a country to be rebuilt following two world wars, it didn't much matter how insular and conservative Americans wanted to be, they still had enormous clout. But with a modern world which has unprecedented travel of both physical bodies and (especially) information the xenophobia of yesteryear is more outdated every day. The cultural and racial makeup of America is changing and changing fast, and the 1950s will never come back. For which I am eternally grateful.