Would the US army side with the citizens in a civil war?

The Oath of Enlistment says:

I, _____, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God." (Title 10, US Code; Act of 5 May 1960 replacing the wording first adopted in 1789, with amendment effective 5 October 1962).

and

Art 94 of the UCMJ says:

(a) Any person subject to this chapter who–

(1) with intent to usurp or override lawful military authority, refuses, in concert with any other person, to obey orders or otherwise do his duty or creates any violence or disturbance is guilty of mutiny;

(2) with intent to cause the overthrow or destruction of lawful civil authority, creates, in concert with any other person, revolt, violence, or disturbance against that authority is guilty of sedition;

(3) fails to do his utmost to prevent and suppress a mutiny or sedition being committed in his presence, or fails to take all reasonable means to inform his superior commissioned officer or commanding officer of a mutiny or sedition which he knows or has reason to believe is taking place, is guilty of a failure to suppress or report a mutiny or sedition.

(b) A person who is found guilty of attempted mutiny, mutiny, sedition, or failure to suppress or report a mutiny or sedition shall be punished by death or such other punishment as a court- martial may direct.

However, a Service Member is NOT required to follow an "unlawful" order:

Anything that is against the Laws of Armed Conflict (LOAC), the Uniformed Code of Military Justice (UCMJ), American Federal Law, and the Geneva Conventions, and possibly local laws. This includes, but is not limited to, failing to attempt to stop unlawful actions and being ordered not to report unlawful actions that you have witnessed.

For example, a superior officer orders you to fire on a church that has not displayed any hostile actions (such as firing at anyone, or harboring the enemy). That would be an unlawful order which you would be compelled to disobey.

At Kent State the National Guard opened up on the unarmed students. I would say they did not side with the students.

During Katrina the OK National Guard went along with the cops, door to door, confiscating guns. I would say they did not side with the citizens either. On the flip side, when the Utah National Guard heard about what was going on in New Orleans they as a group said they would refuse any orders to confiscate guns. Turns out the confiscation was unconstitutional and laws have been passed since then that a natural disaster shall not be used as an excuse to confiscate guns.

I think bottom line you do not know. I do think Obama feels the military would live up to their oath and therefore he wants a "civilian security force" equal to the military in size and funding which can be used to keep us under control. FYI they have been very actively giving machine guns, armored vehicles and 50 cals to even the smallest podunk police department. And even the smallest podunk police department seems to have a SWAT team these days. I would worry more about the militarization of our cops than the military personnel.

Which citizens?

A civil war indicates there is one set of citizens facing another set of citizens

No matter what crazy crap the Government did...there would be a sizable portion of the citizenry that would support it...because they elected them into office

For example today...for every person that doesn't like the current administration....I can find one (usually very vocal at that) that thinks this is the greatest President that ever lived...and nothing will change their mind

I think it would depend on how bad and tyrannical the government really was. I think a lot of soldiers would find it in their hearts to help the citizens. After all, we do have the right to revolution.