I have read the the Enclave was the reminatnts of the Goverment after the Great War.

My question is: Who made up the Enclave in their beginings, only the Goverment, or the majority of the USA Millitary as well?

I ask because the Enclave seems to have a massive millitary influence in the way they behave, and they are extremly well organized (look at Navarro, and their drill master there). I know that the BoS is made up of the US Millitary, but I thought it was just a very small number of soldiers that rebeled once they found out about the FEV (Their leader being that Maxson guy).

Does anybody know who made up the Enclave (If anyone more than the US Army)?

http://fallout.wikia.com/wiki/Enclave

Go to the origins section and it tells you how it started.

I always assumed it to be formed primarily out of the government "elite". The President, his Secret Service, top CIA agents, as well as high-ranking military commanders and generals. I would not say that the actual armed forces were part of this in any way, just the ultimate powers in the American government. And you're right in that the Brotherhood of Steel was just founded by a detachment of soldiers led by Maxson who travelled to the Mariposa base.

What you do have to understand however, is that all of these powerful government types do have some influence over the country's defenses. They may not all fight in war, but they do probably have access to all the nuclear launch silos, still-functioning orbital satellites, and all sorts of other military tech.

That makes a lot of since, but there are so many Enclave soldiers (and they have arounf 10 bases (There is a map in FO2 that has dots showing Enclave base locations, 1 being in California (Navarro), 1 in DC (RavenRock), and 1 off the coast of California (Oil Tanker thingy).

There must have been a tons (Nearly 10,000) of Enclave at the start of the war if there are 10 Enclave bases (If they hold 1000 people each). There must have been more than just the "Important Elite" of the USA.

Whoa, where's that??

http://fallout.wikia.com/wiki/Main_Page is such a wonderful place to learn all things Fallout

No one "set up" The Enclave. It's the exact same thing as the pre-war US government. The soldiers are probably those who used to guard the Pentagon. The civilians were the families of the politicians who evacuated into the Oil Rig.
Nothing really changed.