Why does the American form of government work?

Short and sweet, because of the checks and balances system of power and elected power. Madison designed a system in which he separated parts of government in order to make a base for the government. Not only are there the three branches (judicial, legislative and executive), but each of those also have checks for example the strongest branch is split into house and senate. This was to make each branch independent  and without pull on the other branches as he says "if men were angels, no government would be necessary". So it is with separate of power that our government works as no one person or entity holds 100% control. M adison also deals with factions through country-wide elected positions that would make it very difficult for members of certain factions to control any one branch or cluster of positions.Thus then checking the power of these factions without taking away their liberty.  With all these puzzle pieces aligned the government works as a well oiled machine( most of the time).