Judy Greer has made around 80 movies over almost 15 years in Hollywood. But she appears to be oblivious to the protocol of the actor interview. She comes into the restaurant, makes the "there you are" hands gesture, as if we're old friends finally managing to meet up for lunch, and launches straight into confessional mode: "Oh my God: I totally just had like a 10-minute conversation with someone and I've got no idea who they were."

She also says "fuck" a lot, which strikes an odd note in this place – a muzak-oozing timewarp of a midtown Manhattan restaurant, all obsequious waiters and swaths of peach linen. Halfway through an answer she breaks off to frown at her finger and announce: "I just ate some of my own skin by the way. I'm so gross."

Greer's latest film is Playing for Keeps – a cliched romcom in which a string of soccer moms throw themselves at nonplussed everybloke Gerard Butler, a washed-up footballer moping after his ex wife. She is in good company, working alongside Catherine Zeta-Jones and Uma Thurman. Greer plays Barb, a new divorcee who is desperate to please, and who dissolves into tears every time she trots up to Butler on the soccer field. She makes the tiniest of grimaces when I mention the film, but has many very generous things to say about its director Gabriele Mucino, and Butler. She thinks the latter is "kind of an artist" (and, perhaps less pertinently, that "his eyes are really pretty").

She adds: "I'd been dating my husband for about a year and I'd already kissed George Clooney, Ashton Kutcher and Gerard Butler. Awesome year, right?" She high-fives me and shouts a "Sorry, honey!" to her absent husband, Dean Johnsen, a TV producer whom she married a year ago. She shows me a wedding picture, with Johnsen's teenage son and daughter: "Here's my family that I married! Aren't the kids gorgeous?"

Right now, her husband is having to cope with her the requirements of her Broadway debut, Dead Accounts, which, as she puts it, requires her to "totally make out with Norbert [Leo Butz] every single night. I really can't imagine having to watch him kiss someone else every day – I'd be, 'Dude? Gross. Like, really?'"

So what was her audition for Dead Accounts like? She puts a hand to the side of her mouth, winces, and stage whispers: "I didn't have an audition! I'm so embarrassed!"

Embarrassed because "I really do believe that if I would have auditioned for this role I wouldn't have gotten it. At first I thought, 'Oh, I've got this,' and then, as we dug deeper, I was like, 'I don't have this and I have no idea who this person is and I have no idea how to turn myself into her because she's not like anyone I can relate to.'"

She has clearly found her way now; the New York Times called her "chic and glowering", but, as she tells it, it's offstage that she's floundering.

"My assistant stage manager found me before the show yesterday and she was, like, I have to have a really weird conversation with you. She said: 'I totally forgot to tell you this and I feel terrible: you've never done Broadway before so you don't know that you are supposed to tip your dresser and your hair stylist. And I was like, whaaaat? I feel so bad. I had no idea.'"

Hers is a self-mocking ditsiness, which disguises a focused intelligence and brilliant comic timing. When she talks about her dog, for instance, she says, very sweetly: "Um, here's a picture of him having a nap." I'm all ready to coo at the phone screen and there in front of me is a picture of a bulldog that you would be embarrassed to look at on your office computer. He's asleep on his back and there is no doubt that he is indeed a he.

"I remember making the choice to make people laugh," she says, "because I was a very late bloomer. I looked kind of weird for a long time. It was easier to be the funny friend instead of the pretty friend. I just didn't have the curves that most girls have, until very late, and I have really frizzy hair, and I had braces. I took ballet dancing for ever and there was a natural transition into acting."

Greer was born in the suburbs of Detroit, the only child of her parents, a mechanical engineer and hospital administrator. After graduating from De Paul's theatre school in 1997 she moved to LA and hasn't been out of work since.

"A couple of years ago I decided I really didn't want to be the best friend any more so I told my agent, I'll let you know if I need money but can we try and look for some different things. I was getting bigger and bigger best friend roles but I was sick of being everyone's best friend all the time! I'm constantly getting asked by people on the street: 'How come you don't want to star in movies?' And I'm like," – she does an eye roll so heavy it's made by her whole head – "Really? Why would I not want to star in a movie! People ask me that as if I'm turning them down."

It is a bit mystifying; she's hilarious and she's also gorgeous: wide-spaced, almond eyes, retrousse nose and the naughty grin of someone who enjoys showing people pictures of her dog's penis. So why hasn't it happened?

"I genuinely don't know. I'd like to ask every producer in Hollywood. Maybe I'm not … maybe I'm just not like a leading lady? But I think leading ladies are changing …" She mentions Bridesmaids, last year's widely and rightly loved Kristen Wiig comedy.

"These girls who work at the cupcake shop by my rehearsal space were like: 'Ohmygod we love you, we love you. You were in Bridesmaids and you were so awesome!'" And I said: 'I wasn't in Bridesmaids. I promise you, I wish I was in that movie, I am not in it.' Another person said, 'Oh you were in 27 Dresses!' And I said, 'Yeah!' And she said: 'That was my favourite movie until Bridesmaids came out and now Bridesmaids is my favourite movie!' And I was like," – she mimicks feeble enthusiasm – "yeah!"

Greer turned 37 last summer, but says she isn't anxious about getting older. "I played a mom in this movie Marmaduke, which about seven people saw, and I was like, 'Ugh, I'm playing the mom and now I'm the mom,' and I was totally thinking of it as the end of my career when really it's the beginning of another phase.

"You know, the truth is that the actresses who I look up to are either my age or a few years older or a lot older. And they're all working! I do think that the more women who keep making projects happen, the better roles there will be for women. I mean, men are awesome but they're pretty easy to figure out; women are way more complicated, and way more interesting."

Greer is probably best known for her part in Arrested Development, the anarchic TV comedy which originally aired for three seasons and has inspired cultish levels of fandom. She played Kitty Sanchez, assistant to Jason Bateman's Michael Bluth, whom she's fond of flashing with the line: "Say goodbye to these!"

She was in LA a few weeks ago, shooting one of the 10 episodes of a new series of Arrested Development, to be shown on Netflix, and told Mitch Hurwitz, the show's creator: 'Oh, yeah, thanks by the way for all the people flashing their tits at me all the time,' And he was, like: 'What? Do people do that?' Yes people fucking do that. That's all they do. I get flashed all the time." Then she adds: "It's mostly men."

The show is undoubtedly brilliant, but why are its fans so intense?

"My theory," she says, "is people feel bad because they didn't watch it when it was on TV. And they watched it again and then they were like: 'Fuck! I need more! How can I make up for the fact that I only Tivo-ed it!'"

The interview has drawn to a close. I turn off the dictaphone and thank her. "Now what?" she asks. "Do I just leave? That doesn't seem right!". She thanks me "for the hot bevs", and gives me an energetic squeeze of a hug before she bustles out.

Please, Hollywood, just give her a lead role.

• Playing For Keeps opens in the UK on 1 January