As the title infers, the US Constitution does and doesn't work as it was intended. Set aside amendments and this is how the Constitution as it was finally written after numerous compromises and arguments (probably no two Founding Fathers had the exact same view)- the entire executive branch was written with the express idea that one man would be the first president, GW. The House and Senate were assumed to take Robert's Rules of Order (or some suitably close alternative, Jefferson's Manual was eventually written, and while it was intended for the Senate ended up being used by the House to this day and not considered authoritative by the Senate) and that as the Constitution states create their own officers. Party politics not having quite taken shape in these United States until GW was actually in office, it was not assumed there would be two opposing blocks and the one with the largest number would have the presiding officers.
The Vice President as the President of the Senate was assumed at the writing of the Constitution that he'd actually be "President of the Senate" and equivalent to the House's Speaker; John Adams' arrogance and Senator's contempt of him led the Senate to make the VP position basically honorary and the Senate never adopted Jefferson's Manual like the House did. Whereas House rules are adopted pretty much whole from one Congress to another at the beginning of the session, the Senate rules are more like "we choose to work today in the manner we did yesterday unless 50%+1 decides to change it".
The Constitution does not give the Supreme Court (SCOTUS) the right to declare a law unconstitutional. This was Marbury v Madison that SCOTUS decided "we don't want to rule on the case, but if we did, we can, and in the future we can declare any act of Congress or executive branch unconstitutional". The Constitution assumed that Congress would only pass laws that were Constitutional or else 50%+1 would not have voted; in the case that they did pass one that the President (the thought being that GW being an honorable man would only veto if he thought it was unconstitutional and not for political reasons!) would veto it; if GW got it wrong then of course the 75%+1 of each house would would of course be able to spot it and override the veto! Checks and balances. Just because each branch was separate and there were checks and balances did not mean that each branch could or should check and balance every other branch. Sequestration (impoundment), not in the Constitution, worked just fine until Richard Nixon used them for political reasons and not "fairly" as custom required, resulting in the Impoundment Control Act of 1974. It was always assumed that, especially the President and Senators, would be upstanding honorable capable men.
So, my WI is this- what if the VP was not John Adams, perhaps John Jay, the Senate adopts rules of order as the House does, the VP has Speaker-like powers, can't butterfly away political powers so the House looks the same but the Senate is more controlled (probably no filibustering now as one consequence). And the other change is that SCOTUS can not override Congress or the President (which is the biggest change).