A stage actor and a performance Artist in New York's East Village during the 1980s, she enrolled in the Graduate Filmmaking program at New York University's prestigious Tisch School of the Arts in the 1990s. Winner of a Guggenheim Fellowship for filmmaking, Jenkins also attended the Sundance Institute Screenwriting and Filmmakers Lab.

Jenkins began her career with a short film, 1991's Fugitive Love, which screened at the Sundance Film Festival. Afterwards she completed a congressional mandate associated with PBS to bring diverse programming to public television, that was funded by the Independent Television Service. Another black and white short film, 1993's Family Remains, followed, which earned her early acclaim; it received a Special Jury Prize for Excellence in Short Filmmaking at the 1994 Sundance Film Festival.

In addition to her work in film, Jenkins' writing has been published in Zoetrope: All-Story and Tin House Magazine. Most recently her essay, "Holy Innocents", appeared in the book Lisa Yuskavage: Small Paintings 1993-2004. She has also directed theater at The New Group, worked with teens creating a sex education film for the non-profit organization Scenarios and directed a series of public Service announcements for Amnesty International.

Her debut feature film, 1998's semi autobiographical Slums of Beverly Hills which she both wrote and directed, played at both Sundance and the Cannes film festival. Based on her own experience growing up in Beverly Hills in the 1970s, Slums is a dark comedy about growing up broke in glitzy Los Angeles. Using photographs Jenkins had kept from her time at Beverly Hills High School, Art Director Scott Plauch and Production Designer Dena Roth were able create an accurate period depiction of Beverly Hills, while also staying true to the autobiographical element key the film's success. Starring Alan Arkin, Natasha Lyonne and Marisa Tomei, the film was nominated for two Independent Spirit Awards (Best First Feature and Best First Screenplay) and has since become a cult hit. Jenkins took a nearly decade-long hiatus to complete her next feature film. In the nine-year gap between her two films, she worked on an eventually abandoned screenplay about Photographer Diane Arbus. Before returning to her next feature film, Jenkins branched out to explore theater, essay publications, and non-profit film and TV work. In 2003, Tamara directed The New Group's theater production of A Likely Story, written and performed by David Cale.

In 2002, Jenkins married Screenwriter Jim Taylor, the writing and producing partner of the Director Alexander Payne.

Shortly after her marriage, Jenkins went to Yaddo, the artists' colony in Saratoga Springs, New York, to work on her next screenplay that would eventually become 2007's The Savages. For this tragicomedy about a dysfunctional family dealing with the aftershocks of its patriarch's elderly dementia, Jenkins took inspiration from her experiences with her grandmother and father, both of whom were in nursing homes with dementia. Jenkins' father, who was much older than her mother, first needed care when his daughter was in her 30s. Additionally, Jenkins built upon her theater work at The New Group, departing from her previously straight dramas to something far more absurd. The film layers a bright, doll-like color palette upon a bleak and often morbid story, relying on the Savage wit of her screenplay to tie the film together.

Her next film Private Life, starring Paul Giamatti, Kathryn Hahn and Molly Shannon and also written by Jenkins, was due to begin production in April 2017 for Netflix.