When director Roland Emmerich approached the 35-year-old New Yorker about a role in his blockbuster White House Down, for example, she declined. She had given birth to her second child, Gloria, four weeks previously and was in no mood to trade bath time for battle stations. "I really didn't want to do the movie at all," she says when we catch up in a Mexican hotel resort where she and fellow cast members Jamie Foxx and Channing Tatum are conducting press duties.
"When Roland asked me, I was, 'No way am I going to do this. I have a tiny baby.' I wasn't thinking of working at all, let alone on a huge movie that would take such a long time, but he completely charmed me and convinced me."
The secret to Emmerich's success was the role. "Even though it is a big, wild movie, I think Roland wanted my character to be real and he never wanted her to be the girl who is tied to the railway tracks, the damsel in distress," says Gyllenhaal.
"I think the part and the character are unusually complex and interesting for a huge summer action movie. I hope she's a real woman. She is not in the situation of the girl in the bikini on the yacht."
Far from it. Being the, as she puts it, "girl in the bikini" is not really Gyllenhaal's style.
The actor broke through with the 2002 film Secretary, a movie in which her seemingly submissive character is in full control and Gyllenhaal herself has retained plenty of power in shaping her career, becoming a bona fide indie queen, who rarely takes the big blockbuster bucks.
In the wake of Donnie Darko, in which she featured alongside younger brother Jake, and then Secretary, came the likes of Stranger Than Fiction, Trust The Man, World Trade Center, Sherrybaby, Crazy Heart and, most recently, the period comedy about the invention of the vibrator, Hysteria.
In fact, the last time she starred in a film the size of White House Down was back in 2008, when she appeared in the Batman sequel, The Dark Knight. Funnily, enough, she had just had a baby then as well.
"On The Dark Knight everyone was so understanding about the baby situation," she says, "and with White House Down, too, everybody knew what they were getting with me at that point and they made everything really comfortable for me and my family."
Gyllenhaal, a chatty and enthusiastic interviewee today, is married to An Education and Jarhead star Peter Sarsgaard. The couple tied the knot in 2009, almost three years after they had their first daughter, Ramona.
"There would be days on White House Down when there were thousands of extras and things on fire and I would say, 'I have really got to go and feed my baby now,'" she says with a laugh.
Born in New York City to filmmaker Stephen Gyllenhaal and his producer wife, Gyllenhaal studied at Columbia University before enrolling at the Royal Academy of Dramatic Art in London. The couple now live in Park Slope, Brooklyn, having left Manhattan a little over five years ago because of overbearing pressure from the paparazzi. "I want to go even farther away," she says of her locale. "Honestly, I feel confused by walking around the street and having people take pictures of my children.
"I don't know how to organise that, to be honest. I know it's like part of my job, and I do try to be cool about it, but it is hard for me. Because of that, a part of me wants to go and live a long way away, and then just pop in when we have to work.
"And nothing shoots in New York or LA any more, so it doesn't really help that much to live in either place. But at the same time, I am going to do a play in New York in the spring and I love that I can do that and be home. New York is pretty great and all my friends live there."
Her life on the east coast is similar to that of any wealthy working mother. "Mostly at home I hang out with my friends," she says of her downtime. "We will go to dinner or we will see some music or something like that."
She also spends plenty of time at the gym, with yoga and aerobics topping her exercise schedule. "Doing aerobics is very outside my personality, but I love it," she says. "You work out to the Top 40 and I dig it. I do. It totally chills me out and makes me feel good.
"My husband is a serious, serious runner. He runs 15 miles a day. I have tried running with him but I can't run that much. I get kind of bored. I like pretending I am in Flashdance."
When she's not reliving Jerry Bruckheimer's 1980s romantic dance drama, Gyllenhaal tries to ensure her family lives as normal a life as possible. Her eldest daughter, for instance, attends a local school. "I like the community that my daughter has in school; it is so important and the socialising that she's been going through is amazing.
"To hear her talk about her friends and this one and that one, and these two are getting married, and all these kids' things, it's really important to her."
But Gyllenhaal's career is important to her, too. "There is an actress I admire," Gyllenhaal continues, "and she said if you have the opportunity to do something great, and go somewhere amazing, just take your kids out of school for a little while and do it."
She took her children to New Mexico and Ireland for her forthcoming movie Frank, where she stars opposite Michael Fassbender, and she took the family to Montreal in Canada for White House Down.
"It was hard," she concedes. "It was my first time with two children, so maybe it will get easier. It is a completely different universe each time you have a child. Right now I am trying to figure out how to work and to be a mother of two and it is really hard, mostly because of the travel.
"That's what I find the hardest with the two of them. With one child, who wasn't in school, it was manageable and I would just take her with me. She loves to travel, she loves the hotels, and she's very open that way. But now with two, and with my older girl in first grade?
"I read a project recently that I thought was fascinating and pretty incredible, but it shoots in three countries. Because of that I probably can't do it."
On White House Down she would fly back and forth between Montreal and New York. "It is very manageable in that way. They would happily let me go. That didn't surprise me."
The thing that did surprise Gyllenhaal was Roland Emmerich himself. The German filmmaker is best known for directing big spectacles like Independence Day, The Day After Tomorrow and 2012.
"I had seen some of his movies and I had met him and I didn't know whether acting was particularly important to him," she explains. "But he was so good at directing me, such an expert. I thought that I may have to carve out my own space but he pushed me so hard and was so inspiring and exciting. I didn't know about that him."
In White House Down, audiences meet Gyllenhaal's character when one of the film's two leading men applies for a job at the White House. Tatum plays John Cale, who's pitching for his dream position of protecting the president of the United States, James Sawyer (Foxx).
"In the beginning you see that I am divorced and I am not very happy," Gyllenhaal says of her character. "I put everything into my work and then, pretty early on, I bump into Channing's character in a hallway and it turns out we are ex-lovers and it is kind of electrifying.
"I am in this real position of power in the secret service and Channing's looking for a job and I interview him and realise that he really is not qualified."
Events then crank up a notch when Tatum's character takes his little girl on a tour of the White House just as a heavily armed paramilitary group storms the building. Then, with the nation's government falling into chaos and time running out, it's up to Cale to save his daughter, the president, and the country. Action, explosions, tumbling helicopters, a machine-gun wielding president and a potential love story all battle on to screen.
The actor, meanwhile, believes her strong character might stimulate interest among female audiences. "I hope so," she says. "I just tried to make her a real woman that women can relate to. I also think that Jamie and Channing are pretty cute so that'll help, no doubt."
While she is no stranger to big-budget filmmaking - she shot The Dark Knight while caring for her first child - Gyllenhaal is better known for her independent films.
"For me it has really been project to project," she says of her career path. "It's not a progression toward bigger to bigger to bigger. It's a case that some films are big, some are small, and I decided to do this one because this woman was fascinating to me.
"And, of course, I am interested in a movie that millions and millions of people will see."
Fewer people will see her next film, even though it appears a more natural fit for the indie-styled actor, Gyllenhaal having recently wrapped on Frank with Fassbender and rising star Domhnall Gleeson. The film is a quirky comedy-drama set in Ireland, focusing on Gleeson's young musician who bites off more than he can chew when he teams up with Fassbender's madcap musical group.
"It is a tiny Irish movie and it was really musical," Gyllenhaal says of Frank. "It's about this really super out-there band; Michael Fassbender and I play these soul mates who are brought together by how totally out-there we are."
The movie requires Gyllenhaal to demonstrate musical prowess. "I play all these synths, I sing and I play the theremin," she says, the last a reference to an early electronic instrument. "It was really cool for me. I am pretty musical. I am not brilliant at it - I couldn't be a professional singer - but I really enjoy it."
She also enjoys her life on stage. In 2009 she starred in an off-Broadway production of Anton Chekhov's classic Uncle Vanya and in 2011 tackled his Three Sisters. Next spring she'll tread the New York boards once again with an adaptation of Penelope Skinner's The Village Bike.
"It is a really good play," she says of her new endeavour. "For me with theatre, I don't want to do a play unless it just knocks my socks off, because it's the same thing every night."
The play sees a pregnant Becky (Gyllenhaal) feeling frisky but unable to get the attention of her husband. She subsequently acquires a bicycle and heads out on a journey of awakening.
"Sam Gold is directing it," she says. "He is young - he's my age - and he is the new really exciting director in New York. I think it will be really cool."
The title means what you think it might. "It's pretty promiscuous," she giggles. "It's off-Broadway. It's really not Broadway material."
When we meet, rumours also abound that Gyllenhaal might get frisky on the big screen, too, taking on director Sam Taylor-Wood's adaptation of the steamy bestseller 50 Shades Of Grey.
"Nobody has asked me to do that," she counters. "I think the rumours are probably because of Secretary. Who knows?
"I don't even really know all that much about it, although I want to. I have a friend who told me it was really sexy." n
White House Down (12A) is out on September 6.