Although some have called Willy Loman a tragic hero, he certainly also fits at least one definition on an anti-hero; that is, a protagonist in a literary work who lacks traditional heroic traits such as courage and idealism. You have suggested in your question that Willy may be “passive” or “ineffectual,” and we see many examples of these unfortunate characteristics. Willy lives in a dream world where he is successful; he lies to his family and spends money on a mistress he hopes to impress with his personal fantasies.
Willy is obsessed with being liked and admired—certainly a passive obsession—instead of doing the hard work it takes to become admired. He pressures his son Biff into being the person he, Willy, sees himself as, and denigrates Bernard (the neighbor) for earning good marks in school. Willy sees popularity and shortcuts as the routes to success rather than hard work and effort. He exaggerates his past accomplishments as he continues to retreat from reality.
While it is true that forces outside Willy conspire to take everything from him, he remains a passive victim of the society that values "being number one." He buys the dream he cannot achieve and eventually, in taking his own life, betrays his family again (as he has already done through the marital infidelity discovered by Biff).
What lies at the heart of the anti-hero view of this play is the dishonesty, deception, and self-deception that exists throughout the play—in Willy’s infidelity, in his grandiose perception of himself as a “salesman” (you might ask what he is really selling), and in the self-perpetuating family myth of the American Dream.