Most of us have probably learned in school about how the three branches of government, as defined in the Constitution, are intended to be equal partners with clearly defined roles. If pressed, many Americans could probably specify that the legislative branch sets laws, and the executive branch runs the government. But ask most Americans which is more powerful, or which is the leader of the nation, and everyone will immediately say the President. (The same will apply on the state level with the Governor, and probably anywhere else there's a legislative/executive split.) Even those who know better are still in the habit of thinking of it that way; and since everyone thinks of it that way, over time, it has become that way.
But the Constitution still spells out a design in which the legislative branch is the primary place where decisions are made about the direction that the "ship of state" will be sailing on. And the executive branch's primary job is not deciding where to go, but running the ship, making sure we get there and everything's still in ship-shape when we arrive. These roles are not wholly separated: how you do something shapes the outcome (hence the phrase "executive decision," the first word of which is not an accident), and you can't decide where to go in ignorance of how you can get there, but the roles are nevertheless distinct in intent.
While these roles have drifted away from that intended by the founding fathers, the original roles still have their impact: most notably, the executive branch is still responsible for running the ship, even if it's also expected to provide a lot of the leadership and setting of a course.
It seems to me that the Republicans gain more benefit than the Democrats do from this shift in roles. Time and again, the Republicans put forth a candidate who is clearly unqualified to run the ship, but no one cares, because everyone's forgotten that that's what the job is about. Instead, they're advanced based solely on the direction they intend to steer the ship, even without professing any particular plan on how to get there -- as if the plan is the job of someone else.
As a result, it seems every time we have an outgoing Republican executive branch, they always leave behind a terrible mess for their Democratic counterpart to clean up. Whether it's a devastated budget, a trashed economy, a mass of civil rights issues, a pile of failed policies, or most commonly a mix of all these and more, the messes they leave behind are solidly rooted in the "run the ship" side of things, not in the "set the course" side. Democrats then have to waste most of their time cleaning up the mess left for them, doing vitally necessary but unglamorous things, and getting little credit for it, especially since they inherit such a huge pile of neglected and sabotaged crap that no matter how much they get done they always look bad for how much more there is to do. Which sets the Republicans up for another victory since they provided the illusion of leadership while trashing the ship, but the Democrats provide the illusion of ineffectuality while cleaning up the trashing.
It's a masterful strategy, provided you only care about winning, not about making the country (or state, or whatever) solvent, strong, and able to deal with its problems. But it all depends on everyone remaining either ignorant of, or at least forgetful of, what "executive" is supposed to mean. Fortunately for the Republicans, strategies that require ignorance never fail to get all they need.