Suppose the founding fathers had invented the semi-presidential system, closely emulating the British system, but as a Republic; and the concept of party lists from a single multi-member constituency was made the method of electing parliament as an amendment to the constitution sometime in early 1900s.
As the government stands: parliament is divided into two houses, the House of Representatives and the Senate; as previously stated the House is elected via party lists with the entire country acting as a single multi-member constituency; and the Senate is elected OTL constitution originally had, appointed by the states. The Prime Minister can be from either house, but in practice is almost always from the House; the cabinet works the same way; but the president has a reserve power (which has never been used) to allow him to appoint a Prime Minister contrary to the will of parliament.
The president takes an active role in government; routinely refuses executive assent (vetos) to acts of parliament; and has most of the reserve powers the British monarch has, but is not as tightly bound to the wishes of the cabinet, due to the fact that he is popularly elected and is constitutionally only responsible to the people.
The supreme court is similar, though it is called the Constitutional Court and has been confined to powers solely in the interpretation of the constitution. The Senate has a power similar to the British House of Lords as a court of last resort...
What is politics like today, assuming as few butterflies happened as possible? Who were the American presidents and Prime Ministers? How would having a parliamentary system helped in recent history? How would it have hurt?