Ping, if the politicians had not been involved, the war would have been over very quickly. The US would have bombed the snot out of the North and made a massive invasion. Game Over.
Instead they dicked around fighting a limited war, and wasted time, money, and human lives.
Kieran makes a good point about the threat of WWIII, and this was certainly a factor for the politicians, but the increasing public resistance to the war was a bigger factor IMHO. The number one goal of any US politician is to get re-elected. Everything else follows from that.