The US should have a leader who is technically the head of the country but whose powers are basically ceremonial. He should swear in the leader of the house, appoint certain high-ranking officials (on the consent of the house leader) and sign laws into effect. He could be the one sent to other countries as a representative of the USA, and he'd be welcomed with red carpets, etc. But, he couldn't actually enter any negotiations or anything. He could even wear a military uniform to look extra cool.

In short, the US should have a King.