She plays Cathy Jamison, a Minneapolis mother recently diagnosed with stage four melanoma.
Linney, who is also the executive producer of "The Big C," said on "The Early Show" Monday making the shift to series television was a big commitment.
"It's a world I don't know very well, the series television," she said. "I've done a lot of TV, but never involved in a series from beginning to end. So, it was -- it was a big decision. But I'm so glad I made it."
Linney said the story of the series drew her in because of the things she was thinking about on a personal level.
"(The show's story) sort of coincided with all the things I had been thinking about intensely anyway. Just in my life. About time, the time we have, what to do with our time, the choices that we make. The relationships that we either spend time on unwisely or wisely. So, when it came to me, there was something that said, 'You have to pay attention to this and it might be a good way to sort all this out for myself.'"
Linney said the story addresses aging in a way that looks at it as if it were a gift.
"The privilege of aging, which is, I think, something that people have forgotten about," she explained. "I think it's human nature to sort of push that aside, but, you know, no one is guaranteed a long life. People forget that. That as difficult as aging is, as horrible and frustrating and painful and embarrassing as it can be for some people, you know, it's truly -- it's truly a privilege."
Linney's new series also looks at a topic viewed in a serious fashion with a comedic flair. Linney told "Early Show" co-anchor Erica Hill laughter is a way to cope.
"I think it's survival," she said. "I think it's the only way for some people to survive when the human spirit is tested to such a degree. When you're threatened, when there is huge regret, when there's fear. I think comedy comes in and is a real salve."
As for the portrayal of the character, Linney says she put a focus on the changes her character makes in her life following diagnosis.
Linney said, "I started thinking about, you know, if you have the information that you only have a limited amount of time left, is that a blessing or is that a curse? Does that work for you or does that work against you? So, the psychology of dealing with a character who's wrestling with that, who then has the opportunity to right some wrongs, to raise her son differently, to try to fix her marriage or abandon her marriage, does -- you know, what does that do to a person on a day-to-day basis?"
In addition to her new Showtime series, Linney will also be back on the New York stage for "Time Stands Still" in September.
"I love being on stage," Linney said. "I love being on stage in New York. I can't be happier about that."