And if the president's party blocks action on the bill via one method or the other and it automatically becomes law?
I really do mean no offense, but this is a terrible idea. Presidents would be using it to screw with the opposition party come election time like you wouldn't believe. I would rather the minority party in Congress be given more power to force votes and more rules that force Congress to act in certain circumstances to prevent things like year-long SCOTUS nomination blockades or to prevent power from becoming too centralized (like it is now)
What you're really asking for is more centralization. That's what would make those things happen.
I've been considering if a parliamentary system is better. This seems like a good compromise.
And the President's party could only block a veto on the bill if they had a simple majority who voted to NOT veto it.
Well, not exactly. I agree with the idea that giving power to the president to push legislation could help alleviate some forms of obstruction and gridlock, it's only 1 approach to solving the gridlock issue. It's an approach I do not favor. I favor mitigating the ability to obstruct using changes to the way
Congress operates, and not by introducing a new legislative vector.
I actually like your idea to some degree, but not the auto-enactment if not veto'd by Congress. If I
had to choose some variation of this idea, it would something along the lines of POTUS being able to introduce a bill to Congress if he can get 1/3rd of each chamber to side with him, and by doing this, forcing Congress to vote on the bill with no ability to filibuster. No auto-enactment, but also gives another method to bypass obstructionist methods. Requiring substantial Congressional support means the president can't as easily screw around for partisan purposes. So POTUS + 1/3rd Congress to introduce, then simple majority to pass.
It's a fun thought exercise, but changes to the way legislating works in Congress outside of maybe filibuster reform is almost a fantasy at this current point in time.