I think LBJ did lose some ground with the Voting Rights Act - which he stated was going to lose the Southern Democrats. (It did, they flipped to the Republican Party shortly after it and then found a way to weaken the act years later.)

But you're right...a lot of what LBJ and FDR had was the ability to make back-room deals. LBJ was a master manipulator of the system. As was FDR.

I don't think it's possible to do it today, though... a lot of things have changed since then.