Halfway through “The Assassination of Richard Nixon,” an eerie and affecting new film, Samuel Bicke (Sean Penn) shaves off his mustache. To the depressed and abandoned Bicke, the mustache represents honesty, integrity and decency — the very values he tries desperately to defend — and he only gets rid of it in order to keep his job. Later, Bicke puts on a fake mustache before entering an airport in his psychotic attempt to kill President Nixon. The internal struggles over his facial hair are relatively minute, yet they are one detail among many that Sean Penn makes interesting with his unparalleled skill. With the help of its excellent leading man, this film gets the details right, yet it fails to convince us of its central premise.

“Assassination” is based on the surprisingly under-reported and subsequently forgotten story of Samuel Byck. Alienated from his family and employer, and driven by the violence of the Black Panthers, Byck led a botched assassination attempt on President Nixon in 1974.

In the film, Bicke — whose name is changed to allow for greater liberties — is a struggling furniture salesman who can’t succeed at sales or in his personal life. Growing increasingly frustrated with his failures, he sees himself as a kind of crusader for the working class of America, and he intends to show the powers that be the change that can be made by a mere “grain of sand,” as he calls himself.

The name Bicke is reminiscent of Travis Bickle, the antihero of Martin Scorsese’s “Taxi Driver,” the greatest depiction of violent alienation ever put on film. “Assassination” bears striking resemblances to that classic, particularly in its use of a device to help us hear the alienated protagonist’s inner thoughts. Not shockingly, it ultimately proves itself inferior, mostly because there is little to convince us of the believability of the main character’s decisions.

Mueller’s and Kevin Kennedy’s script is simply underdeveloped, and it suffers too many narrative holes as a result. Bicke’s descent into madness is never quite believable, and his decision to pin his misfortunes on Nixon makes little sense in the context of the film. True, Bicke is surrounded with televisions whose contents fortuitously control the next plot turn, from Nixon’s “I am not a crook” speech inspiring anger in the righteously honest Bicke to the Black Panthers’ speech leading to his sudden belief in violent resistance. But the president is only mentioned once in the film outside of the televisions, in a way that feels like educational grandstanding.

In fact, were it not for Nixon’s presence hovering generically over Bicke’s actions, the story could be told about any alienated man, in any era, who is driven to madness. This is both a blessing and a curse: Penn is convincing as an everyman whose plight is too difficult for him to bear. But for a movie whose title is controversial, political and specific to one era and leader, “Assassination” is annoyingly vague and chronically unclear. The movie takes place in a vacuum rather than in the downtrodden 1970s.

Penn steamrolls over those narrative lapses with his stunningly realistic, heartbreaking performance. He is frequently called the best actor of his generation, and for good reason. Penn consistently picks challenging, dark roles, and finds believability and sympathy in otherwise unlikable characters. Equally remarkable is his talent for adapting himself to a series of violent, disturbed individuals and making each one vital without repeating himself.

It is because of Penn’s visceral performance that the film rises above lifelessness. The supporting characters are barely more than cliches: the estranged wife (Naomi Watts), the loyal friend (Don Cheadle) and the ruthless boss (Jack Thompson). These talented actors are sadly underused, and their roles are pitifully underwritten.

The film’s themes are not anything new, and their treatment is hardly subtle. This is not to suggest that one ought to scoff at the plight of working-class Americans, nor ignore the issues Mueller raises, such as morality in the workplace and the unfortunate role race plays in the business world. The script alternates between perfunctory scenes between Penn and each of the supporting players, as if merely to give respite from Penn’s fiery intensity or to pay deference to the morals of the story.

Despite these qualms, the film is an example of stripped-down narrative filmmaking at its most effective. Mueller’s direction is impressive for its remarkable subtlety, restraint and attention to detail. Veteran Emmanuel Lubezki’s intentionally jittery cinematography, combined with tense pacing and editing, enhance the film’s edginess. The whole picture is bathed in an eerie blue, which increases the claustrophobia of the camera work and provides a suitably creepy atmosphere for Penn to work within.

In the end, the primary reason to see the engrossing and disturbing “Assassination” is Penn’s performance, which stands head-and-shoulders above most work today. But the film is also a self-declaration of an important new director, Niels Mueller, who has the confidence to pull off a challenging film, if not yet the mature writing to match his directorial talent. But he has set a high bar for himself.