Politics have always been at the core of the conflict in the Star Wars Saga. Whether it's at the forefront of the story as we see in the Prequel Trilogy, or taking a backseat to military action as seen in the Original Trilogy, the entire story represents a galactic political struggle.
The Force Awakens isn't entirely different in this respect, although the politics are only referred to briefly. Considering there is around 30 years of political development since the victory of the Rebel Alliance in the Battle of Endor at the end of Return of the Jedi, a little political background in the new Star Wars canon may help to explain what's up with politics in Star Wars: The Force Awakens.
The Following Contains Spoilers for Star Wars: The Force Awakens
All information sourced from Star Wars: The Force Awakens movie, Star Wars: The Force Awakens novelization, by Alan Dean Foster, and Star Wars: The Force Awakens Visual Dictionary, by Pablo Hidalgo.
After the Battle of Endor, the Rebel Alliance reformed itself as The New Republic, and continued its push against the Empire, eventually forcing them to make a last stand at Jakku, resulting in one of the Alliance's biggest victories in the Galactic Civil War. After this, the Empire agreed to sign the Galactic Concordance. A peace treaty that required the Empire to completely demilitarize.
Mon Mothma, the first Chancellor of The New Republic, knowing the Galaxy has grown wary of a centralized government, removes Coruscant as the capital of the republic. Instead, the New Republic capital will regularly change locations as to prevent the concentration of power as had happened in the Old Republic, leading to the rise of the Empire. In a similar attempt to differentiate itself from both the Old Republic and the Empire, the New Republic also drastically scaled back it's military, keeping a loose defense force in place, but no standing army or navy.
Having been completely beaten and de-clawed, the Empire retreated into the unknown regions of the galaxy, where it began to build again, eventually reforming as the First Order. All the former Imperial factories and academies have been seized by the New Republic as a part of the Galactic Concordance, so the First Order started again from scratch. Building new Star Destroyers from new factories deep in the unknown regions, the First Order uses many ships in its new fleet as mobile academies, training all its troops on the move to avoid alerting the New Republic of its defiance.
Not one to be fooled, Princess Leia Organa wisens up to the activities of the First Order and urges the New Republic to once again grow its military and apply more scrutiny towards the rise of the First Order. Ironically, even though she is a hero of the Galactic Civil War, a former Old Republic senator, and Alderaanian royalty, she is labeled as a paranoid warmonger, and the new senate refuses to acquiesce to her pleas.
Taking matters into her own hands, Leia calls upon many old allies of the Rebel Alliance, such as Admiral Ackbar and Major Ematt, and begins to recruit younger members who believe the pending danger of the First Order, including some who served in the New Republic Defense Force, such as Poe Dameron.
Despite mustering up a respectable command of old Alliance leadership, occupying an old Rebel base on D'Qar, and recruiting enough pilots, mechanics, and other operatives to man the Resistance, Leia is unable to get any financial or political support from the New Republic, basically hamstringing the the Resistance force from reaching it's full capability.
Without any accountability to the New Republic, the First Order creates Starkiller base, one of the largest known military constructions in history. Harnessing the power of dark matter, Starkiller base is able to destroy entire solar systems from across the galaxy.
Feeling the pressure from the Resistance, and knowing the New Republic can only be fooled for so long, the First Order initiates the first major strikes against the New Republic, eliminating the entirety of the Hosnian system, including Hosnian Prime, the current seat of New Republic politics.
Although this strike doesn't destroy the New Republic in its entirety, it basically serves as a targeted assassination of the current Chancellor and most of the senate, sending the New Republic into chaos.
The Resistance is able to launch an attack on Starkiller Base, successfully destroying the weapon (and the whole planet), but with an unknown number of First Order Star Destroyers in deployment, and the forces of the New Republic basically decimated, and the Resistance forces still in early establishment, the events of The Force Awakens represent an absolutely massive shift in power for the Galaxy.
This means that Episode VIII will basically reset the Star Wars universe back another Galactic Civil War, except no one faction currently holds the galactic seat of power. We can likely expect to see the Resistance and remnants of the New Republic band together to scramble for control against a First Order that has begun to creep out from the shadows of the unknown regions.