I strongly suspect that Ayn Rand in general and Atlas Shrugged in particular is critical for understanding the agenda of the Republican power structure.
Leaving aside the ridiculous content of Rand's political "philosophy", it's instructive to look at the events and development of her narrative.
John Galt works as an engineer for the Twentieth Century Motor Company. Using his magical powers to completely revolutionize physics, he invents a magic motor that can provide nearly limitless, free mechanical power.
In a heavy-handed allegory to the Bolshevik revolution (in which Rand and her family was stripped of their upper-middle-class privilege) the Twentieth Century Motor Company is inherited by "communists" and turned into a collectivist dystopia.
John Galt is offended by this takeover. Note that he is not actually harmed: he is free to leave and his invention with him (even though one would suspect that the Twentieth Century Motor Company actually owns the intellectual property).
Galt immediately forms the intention of "turning off the lights of New York", an obvious metaphor for the apocalyptic collapse of mid-20th century society.
Galt begins recruiting the most productive people, convincing them to withdraw their productivity from the larger society and begin forming a Utopian society in Colorado. Because the society is not yet self-sufficient, those who withdraw take the menial jobs where the can honorably earn their keep, but contribute nothing of larger value to society. Galt also recruits two important allies, Francisco d'Anconia, who controls a global copper-mining empire, and the pirate Ragnar Danneskjöld.
Narratively, the novel opens about ten years after the beginning of Galt's efforts to bring about the apocalypse. Economic productivity has degenerated considerably, but has not yet collapsed. Hand Reardon has (magically) invented "Reardon Metal"; Dagny Taggard is operating Taggart Transcontinental profitably and undertakes large-scale capital improvements; and Ellis Wyatt has revitalized the economy of Colorado.
Dagny Taggart follows John Galt to "Galt's Gulch", offering the reader a glimpse of the Utopian society that will follow the purification of society's corruption. (While there, Dagny offers her subservience to Galt, another direct parallel to the misogyny of the Christian mythos). In one telling aside, during Dagny's absence a series of incompetent and perverse actions leads to the deaths of a train full of passengers. Rand dwells with morbid fascination on how much the passengers deserve to die.
The government, which has become controlled by corrupt, collectivist and tyrannical elements, undermines productive capabilities. In addition Ellis Wyatt, Francisco d'Anconia and Ragnar Danneskjöld commit acts of sabotage: destruction of oil wells, copper-mining facilities, sinking of supply ships and bombing factories.
After issuing his manifesto, John Galt is captured by the government, who believes him to be their best hope for restoring order and productivity. (Galt is captured because the government is following Dagny Taggart, now his lover, in yet another parallel between Atlas Shrugged and Christian mythology: betrayal of the male hero through the agency of the woman.) Inexplicably, they first torture him, and then offer him virtually absolute power to reform society. He refuses this offer because he does not believe they will implement his suggestions (specifically an end to the income tax). It's notably that Galt does not negotiate in any sense, even to the extent of making demands under threat of walking away; it's clear he intends to walk away no matter what.
Dagny Taggart and Hank Reardon (who prove to be skilled military commandos in addition to their other varied superlative talents) rescue John Galt from the government; as they are escaping, the lights finally do go off in New York.
Additional, the protagonists are explicitly divorced from the political process in any form. Hank Reardon hires a lobbyist, but only with ill-concealed disgust and reluctance, and without even minimal supervision... especially telling for a character whom Rand portrays as finding 25 hours in every day to attend to every detail. The protagonists have no interest in telling their story to the nation or the world, they have no interest in persuading the world to their values. Galt issues his lengthy manifesto at the end of his campaign to bring about the apocalypse, when it is far too late to actually change anything. Galt's attitude is reminiscent of Rorschach from Watchmen: "The accumulated filth of all their sex and murder will foam up about their waists and all the whores and politicians will look up and shout 'Save us!'... and I'll whisper 'no.'"
Atlas Shrugged is a near-perfect instance of the narrative of purity. The narrative of purity starts with a "golden age", followed by a corruption of the golden age, followed by its restoration by eliminating the corruption through the appearance of a messiah. This narrative is, of course, fundamental to the Christian Bible: Eden, the fall of man and original sin, and the restoration of Eden in heaven through the agency of the apocalypse. The key element is redemption through the elimination of corruption, differentiating the narrative of purity from the narrative of power, seen for example in the Koran, where the followers of Allah do not eliminate disbelief but rather achieve (or are exhorted to achieve) domination over the unbelievers.
Of particular importance to the narrative of purity is that corruption cannot be reformed. Corruption is inherent and ineluctable. In Christian mythology corruption exists in everyone, and is mitigated only by supernatural grace. In Atlas Shrugged, the corruption in the antagonists — James Taggart, Lillian Rearden — comes from an ineluctable self-hatred or from a desire for political power — Orren Boyle, Wesley Mouch — apparently fundamentally incompatible with Rand's pure values.
The development of the moral character of the protagonist is the critical element of every narrative, and Atlas Shrugged is no exception, where the focus is on the development of Dagny Taggart's charager. She does not really grow as a character: her development consists, rather, of eliminating her compassion for and submission to those of the "wrong" values. The lights of New York cannot go off until Dagny gives up her attachment to the well being of the larger society; indeed this is the only change in Dagny's character.
Rand is not, of course, the first to employ the narrative of purity; as noted, the form goes back to the earliest history of narrative mythology. Rand is, however, the first to apply this narrative form to capitalism in an explicitly mythological epic tale.
The real world is, of course, considerably more complicated and messy than epic mythology. Still, I think Rand's application of the narrative of purity to the capitalist ruling class can go a long way towards explaining otherwise puzzling elements and behavior of contemporary politics.