Clarifying some things from Discord:
this is not an overhaul of mechanics. This is an extra layer of play. New mechanics, not replaced mechanics.
In other words, the President governs with the consent of Congress but so long as they have that consent they possess vast authority to set the agenda and implement policy at their discretion.
Basically.
You are the one who made it out to be "President against Congress". If it's actually going to be "party or parties control Congress and the leader among them is President", then we should have much more freedom in our actions than you described. Simply because no one would ever get to be President without having a lot of influence over their party, and therefore a strong ability to determine which laws get passed at all.
But instead you made it sound like Congress would pass laws without much in the way of input from us at all and it'll take extraordinary effort to get the influence that in a normal parliamentary system we'd need to have before we ever became the head of government.
Of course you have influence. I specifically lay out the mechanics by which you can exercise it. Your influence just isn't infinite, and you are, influence or not, capable of disagreeing with the majority opinion of Congress. Thus, we now have mechanics laying out how that would be dealt with.
This feels kinda tautological/Ouroboros-like, because IIRC a lot of the character/flavour behind Congress and its political parties originally came from player debate. So now stuff based off of player debate is going to mandate what players do - once the extra steps get taken out it's just players doing what players are/were in favor of doing.
Maybe set up a visible/transparent system/mechanic for QM/populace-generated positions and ideas to be introduced to Congress? Not perfectly, but something along the lines of a rumor mill or opinion poll so things aren't quite coming from a vacuum.
Also, if Congressional factions and opinions are going to be a major factor in play, we as players should probably have better access to knowledge of Congressional factions and politics in the Status screen - party names, percentage support, and a handful of rough descriptors like (Socialist-Social Democrats) just isn't good enough and expecting people to dig through old posts to learn who's in what faction and what exact policies given factions do or do not support isn't really reasonable.
The players do not determine the actions of political parties. I may reference members of the thread for what parties broadly associated with those players' political positions might think, but it very much is me pulling from one of many sources to make my own decision.
Me lifting up
single, specific players to model the actions of parties in Congress is mostly me memeing.
I have no real problem with this, save that we should encourage widespread voting and democratic norms as much as possible, which I'm pretty sure we were already down for.
Frankly, it's been long enough since we started this quest and enough has happened in the real world that I think some of us may have diverged from our initial position. I, for instance, have moved further left and and am considerably more concerned with democratic engagement than I was at the time.
Honestly, as part of the worldbuilding, each of the Revivalist factions takes a different part of the American legend as their founding attribute. The CFC takes the idea of America's democratic legacy as their founding ideal. And, in the process, take it much, much further than the Old Country ever did.
Of course, ideals, reality. There's plenty to be done.