You are exactly right; the ‘right’ uses smoke, the left uses mirrors. We call it a two party system, but it's really a dual deception system. Democrats lie and say that what’s best for the government is also what’s best for the people. Republicans lie and a claim they will do what’s best for the people in spite of what’s best for the government. Between the two of them they trick almost everyone, but they are really just taking turns extracting as much money/power from they country as they can.
The reason they appear to fight is because they only want the power/money/life to be sucked out of the country during their turn to do the sucking. They are not trying to destroy the country, just like a tapeworm doesn’t want to kill its host, but there are so many of them now and we’ve lost control of them, each sacrificing a chuck of our country for their political aspirations.
Unfortunately a new party may not be a solution. As soon it becomes powerful enough to matter it becomes part of the problem. Maybe a bunch of parties, so many that one doesn’t get a majority, and bribing them all is to expensive?
There probably isn’t an easy solution, but I believe part of it is having people on either side of the political debate realize they are both right about each other’s party being no good, and instead of picking their “lesser evil” coming together to fight and take back what’s theirs from their mutual enemy: the politicians.