But before the name-calling, mudslinging, back-stabbing and bloodletting knife-fights materialized, the overjoyed producers of "Saving Grace" awarded the Oscar-winning actress the title role. Within weeks, Hunter was on the set shooting the episode as Oklahoma City Police Department Detective Grace Hanadarko - in bed, stark naked and simulating sex approaching an orgasm with a more subdued actor.
Hunter, 49, has wasted no time making the part her very own. In the wake of horrendous personal tragedy, Grace has made self-destruction a new art form. She sleeps with just about anything male - good, bad or indifferent - but loves Jack Daniels to the last drop.
And then she accidentally kills a man one night by running over him with her vehicle while under the influence of much alcohol. As luck will have it, a seedy-looking, tobacco-chewing guardian angel named Earl (Leon Rippy) gets rid of the body and insists on trying to kick her back on the right track. It's a journey they both come to regret occasionally along the way.
The industrial-strength cast also includes Kenneth Johnson as Detective Ham Dewey, her day-job partner and bedmate on most nights; Bailey Chase as Detective Butch Ada, a professional antagonist; Bokeem Woodbine as a mysterious death-row inmate haunting Hanadarko 24/7; and Laura San Giacomo portraying a religious forensic expert who refuses to judge Grace on any grounds.
"I wanted a change in my work and found what I thought was an incredible story and a thoroughly original character," explained Hunter, who also serves as one of the producers of the television show that marks her debut as a series regular. "To me, she looks at life for its pleasure possibilities and is very comfortable in the chaos of life. She invites chaos; she's a force of chaos herself."
Grace Hanadarko - a wild child with a conscience - is extremely close to her heart and mind, according to Hunter.
"Every character in my career comes from my own life experience, my own imagination and what I've seen of people who made an imprint on me. She doesn't have a husband, children or an extravagant lifestyle. She's a creature of instinct and lives large."
It took a quality project such as "Saving Grace" to lure Hunter from her comfortable home in chaotic Manhattan to unfamiliar surroundings in relatively relaxed Los Angeles, with a two-day stopover in Oklahoma City for exterior scenes. Particularly since it meant moving her entire family - which includes her toddler twin boys and their father, British actor Gordon MacDonald - to the West Coast for at least 13 weeks per year.
"I don't talk too much about my private life," she said, true to form. "I let my life filter through my work."
Born in Conyers, Ga., and reared on a nearby 250-acre farm, Hunter is the daughter of a farmer/sporting goods salesman and a very busy homemaker. While the boys pitched in with all the farm chores, the girls did useful things such as dance and piano lessons. A realist, she knew early on that she had no professional-quality talent for the piano and turned to acting instead.
Lots of high school stage productions led her to earn a bachelor of arts degree in drama from Pittsburgh's Carnegie-Mellon University in 1980; most of her siblings chose sensible careers including that of an airline pilot and a train engineer.
"Growing up on a farm definitely affected my work in a big way," she said. "With so many of us, there was lots of support and a very, very social upbringing."
After a couple of years near starvation (and sharing a tiny flat with Frances McDormand), Hunter made her Broadway debut in Beth Henley's "Crimes of the Heart," then built up her major theater credits with "The Miss Firecracker Contest" and "The Wake of Jamey Foster." Large film roles were launched with "Raising Arizona," and now includes Academy Award nominations for "Broadcast News," "The Piano" and "The Firm."
She also won the Oscar for "The Piano" in the same year as picking up an Emmy award for "The Positively True Adventures of the Alleged Texas Cheerleader Murdering Mom." She had already won an Emmy for "Roe Vs. Wade" - they make a nice pair in her enormous awards collection.
Between making nearly 40 movies, she also married (and divorced) Academy Award-winning cinematographer Janusz Kaminski ("Schindler's List," "Saving Private Ryan").
"My whole career has been ways to explore different women and subject matters," she said. "I kind of look at it as a long conversation with myself."