The creators had Danes in mind when they were writing the Homeland pilot, so much so that in the original scripts the character is called Claire.
"So that was very flattering and a little surprising," she says. "And a little alarming, actually - that it was a role tailor-made for me. I mean, I didn't see myself in that particular light. When I talked to my agent, she said, 'Well, ya know, you'll have a lot to do' - which was a bit of an understatement."
Towards the end of the first series her character experiences a manic episode - a difficult state to portray without risking cartoonishness. But Danes is electrifying, weather fronts of expression rushing over her malleable face.
"I think it's important to never play 'crazy' - you have to know what kind of crazy you're playing. There are very few opportunities to play characters that are this rich, this active. It's a filet mignon of a role."
She's signed up for seven years of it and already garnered a Television Critics Association award; she has also won best actress for the role at both the Golden Globes and last month's Emmys. Mandy Patinkin, who plays her mentor, Saul, has talked about her talent in words extravagant even for the realms of luvvie hyperbole. He recently told the Hollywood Reporter that he would die for her.
"She is one of our great gifts as an artist ... and I am one of the privileged people to get to be with her and learn from her every day."
The show's biggest endorsement, though, has been from Barack Obama, who reportedly requested four copies of the season finale. When the President sat next to Danes' co-star Damian Lewis at a recent state dinner, he told him: "While Michelle and the two girls go play tennis on Saturday afternoons, I go in the Oval Office, pretend I'm going to work, and then I switch on Homeland."
I wonder what goes through his head as he watches. There's one episode in which the vice-president attempts to conceal his government's drone strike on an Iraqi school by claiming terrorists have faked the images of maimed and killed children.
"It's very provocative," Danes agrees. She admits that before accepting the role, "I certainly had questions, if not reservations, because it is so immediately relevant to what's happening in the world. I was concerned that it might become exploitative in some way. But I'm so impressed with how the writers have managed to tell a very volatile story without being reckless.
"The first time I realised I was patriotic was after September 11," she says. She was living in Sydney at the time. "I couldn't have been farther away, physically, from the event, but I grew up in downtown New York, not even a mile away from the towers. One of my friends wanted to have a debate about it and when she was pressing me to take an intellectual position, I just kind of barked: 'my house is on fire!' That's how it felt; it just felt personal and visceral. Growing up in New York with artist parents - a very liberal environment, where we were always encouraged to challenge the status quo - I think for a long time I confused jingoism with patriotism. And that is a mistake."
Danes spent a day with an officer at Langley, the CIA's headquarters in Virginia, and that seems to have fortified her patriotism, too. "They were very earnest in their devotion to the United States of America. I was very touched by that."
And then she switches from serious citizen to excited kid as she starts talking about what the real-life CIA agents do.
"I was just struck by the fact that these spies do really spy-y things! They'll get into a car crash with somebody - they'll literally bump into somebody to initiate and then cultivate a relationship. I mean, in some ways - this seems a little presumptuous and it's not entirely accurate - but actors and CIA agents are [both] migratory and assume different roles. It's very hard to maintain relationships when you are having to conceal so much. They often marry each other - kind of like actors. I mean, who else is gonna get it?"
She speaks from experience: Danes met British actor Hugh Dancy in 2007 on the set of romantic drama Evening, and they married two years later. The couple are about to move into a new Manhattan apartment. A new address must seem like a minor change compared to impending motherhood.
"I've been fantasising about this for a long time. I want to know: who is this person?" She addresses her belly. "I just want to meet this little nugget! Who is this - she, he - gonna be?"
When I ask her about the films she loved as a teenager, she responds: "Oh God - Molly Ringwald. Those John Hughes movies. Oh my God, did I love her?"
People talk the same way about Angela Chase, the sardonic and sentimental heroine of My So-Called Life, the teen TV series that began Danes' career in 1994. Thanks to its appearance on media streaming website Netflix, the show has been granted a new cultural currency by a generation of teenagers hungry for the borrowed nostalgia of oversized plaid shirts and velvet scrunchies.
"There was that whole resurgence of grunge, that 90s revival," she smiles. "It was a good era."
Was she a very serious 15-year-old? "I was, but so many teenagers are serious, that's why they're so hilarious. For a long time I was playing at being a grown-up and it was a slightly confused idea of what that meant. I was all," she frowns and balls her fists, "serious face and phoney moustache. Now I kind of realise that the grown-ups never really knew what they were doing - and that's okay."
The irony of being a teen star synonymous with the angst of high-school life is that you never get to experience that life yourself. "I lived my adolescence on that set, with styrofoam lockers, in some abstracted version of a high school, so I don't really know who I would have been in high school. I didn't have a peer group to figure that out within; it was all sort of suspended."
It sounds like she had a truly terrible time at school. "I was busy being misanthropic and miserable, as most 13-year-olds are. Wuh," she exhales. "God. Yes, that was not a great time. Girls at 12 are horrid. There were so many intricate social rules that I just could not be bothered to observe. I didn't know that you were supposed to dumb down. But I learned it fast when I made myself so vulnerable to ridicule." After a certain point she just ran away from it to act.
"It was such a relief, because I was so ready to borrow Winnie's [Holzman, the creator of My So-Called Life] perfect words and just scream them out: 'F***. Y'all'."
She won her first Golden Globe for the series, and YouTube obliges with footage of 15-year-old Danes hunched behind the podium in her spaghetti-strap dress and making an endearingly gauche speech. A year after this, in 1996, she played Juliet to Leonardo DiCaprio's Romeo in Baz Luhrmann's blockbuster. Soon after, she turned down the role of Rose in Titanic. Chasing stardom never seems to have been her priority.
"I've always wanted to play a woman who drives the story forward, [who] doesn't just facilitate somebody else's story. And you have to be an actor-protagonist in order to do that," she says. "I mean, I also like playing supporting roles, but they have to have some course to take, not just be insipid and attractive."
By 1998 the extent of her celebrity was confirmed with a Vogue cover. "Ivy League Star" ran the strapline: this was also the year that she enrolled as an undergraduate at Yale University. Her two years there seem to have satisfied more of a social than an intellectual need. "I was so relieved at college to discover that people became much less awful - they stopped being assholes after a certain point."
She majored in psychology and says that if she weren't an actor she'd be a therapist. "Psychology and acting are very closely linked. It's just about studying people and how they work. It can be an incredible discipline and exercise. I haven't been in a while - I haven't really needed to - but I'm glad it's there if I ever do."
She first went to therapy when she was 6. A fact which, she protests, has been overstated. "I had these imaginary friends who followed me around and made me do things," she says dismissively. "I don't know - I was a little OCD. But it's not that relevant, not that big a deal."
Acting doesn't seem like that big a deal to her either. "It's not where I experience my personal catharsis," she says. "It's ridiculous what we do, and I find it endlessly amusing. As a young performer, I didn't know that you can have a great time playing someone in terrible crisis.
"The more you know it's not real, the deeper you can go in to it. And the easier it is to let it go when it's done. It means," she shrugs, "you feel much more entitled to your happiness."
The new series of Homeland screens on TV3, Mondays at 8.35pm.
