In what ways did contemporary American literature criticize and reject many of the ideas/ideals that make up the American nation?

American literature in the 1960s was often reflective of the counterculture at the time, which rejected the materialism of the 1950s but pushed further than the literature of that decade (Beat literature, most notably) in its rejection of conformity. The most prominent voices of postwar literature until the 1960s were still predominately white and male.
By the 1960s, with the rise of New Journalism—a form of essay-writing or reportage in which a writer would include him or herself as a part of the sociological experience they were writing about—literature included more white women and black men. Joan Didion began her career in the 1960s, writing about aspects of American counterculture and her personal history of life in her native California. Even popular literature, such as Jacqueline Susann's Valley of the Dolls, dealt with the underbelly of fame and the perceived glamour of life for young white women in big cities. She explored pill addiction and sexual exploitation, which she herself had witnessed during her years in the entertainment industry.
The Black Arts Movement also played a role in rejecting American ideas and ideals. Started in 1965 by Larry Neal and Amiri Baraka (a.k.a., LeRoi Jones), the goals of the movement were to form a uniquely black aesthetic (here, the influence of the postcolonial movement of Negritude is important to note) and to demonstrate how the arts were connected to more universal goals "for self-determination and nationhood." Figures from the movement rejected the "cultural values inherent in western history" and advocated that they either "be radicalized or destroyed," which meant rejecting the literature that was popular at the time (Faulkner and "Dick and Jane"), which they believed reinforced white values, in favor of that which elevated blackness ([W.E.B.] DuBois and [Ghanaian president] Kwame Nkrumah).
However, even in their rejection of American values, countercultural literature still inadvertently reinforced some American values. The Black Arts Movement's call for "self-determination and nationhood" is a call for independence that is intrinsically American, for it is calling for a divorce from an oppressive colonial power and emphasizing the importance of individual expression. Ken Kesey's characters in One Flew Over the Cuckoo's Nest struggle against the oppressive and authoritarian Nurse Ratchet (a symbol of the authoritarian power structure) to experience more personal freedom. Desires for personal freedom and individual expression were predominant in the 1960s and reflected in both pop fiction and literature.