I remember a conservative and effective executive from a quarter century ago who was able to do a great deal despite a hostile congress, without a majority in either house.
But, as mentioned, he was actually conservative, and he was actually effective. It is odd that he is the one who is dismissed as an actor.
Ronald Reagan had a majority in the Senate from January 1981 until January 1987.
We differ in our definitions then. A persuasive, principled, focused and determined president could do much with simple majorities in the house and senate.
Other than budget reconciliation bills which only need a simple majority vote, you need 60 votes in the Senate to end debate! A majority can rule in the House. The Senate has its own rules.