Why is the Republic defeated so easily?

This one may seem the biggest questions of them all, simply because it provides the context of Star Wars: The Force Awakens, while also connecting A New Hope with this latest installment. So the question can be translated in another way: what happened after Palpatine's death and after the defeat of the Empire?

Of course, the answer to this question can be found in the books (and this is the last time we will mention this). The film, on the other hand, gives us no hint "“ in a way, we are back at square one, with a new form of the Empire, now called The First Order, and the Rebels, now called the Resistance.

We can assume that, after the defeat of the Empire, a period of transition was needed, in order to reestablish a working democracy. We can also assume that the followers of the Empire weren't completely eradicated, surviving in the corners of the galaxy, with the First Order being the best example.

But, even if so, how can a small rebel faction defeat a democratic galactic government in a single shot? As far as the movie shows, the First Order has only a handful of Star Destroyers, if it has them at all. Even if they have the Star Killer base, it is still just a singular weapon, which should pose any threat to a galactic fleet.

In this case, we can assume that democracy was its own enemy, in the sense that all the bureaucracy and the complex voting system was the one which prevented the galactic government to act swiftly (one of the deleted scenes has Leia trying to convince the said government to act sooner rather than later).

One other assumption can be that the Republic wasn't defeated, even if its capital was destroyed "“ though having the entire government destroyed surely brings another period of transition, in which all sorts of perils appear and in which, essentially, democracy barely functions.

But these are all what ifs, without any definitive answer provided in Star Wars: The Force Awakens.