For years actor Paul Giamatti was the go-to guy for bit parts.

“They’d say, ‘Oh, you’re right for it. We need a guy to be a bartender or a homeless guy or a cop. So you’re going to be right for it, you’re the guy that’ll do,” he says in a recent interview.

“I’ve always said the easiest thing to be in this business is a white, male character actor because they just need a guy to be the janitor or the senator. A character actor, they’re going to come for you. They know what they’re getting. They know you’re short or you’re bald or you’re overweight. That’s what they’re getting.”

They knew what they were getting until Giamatti starred in the film, “Sideways.” Then, all of a sudden, his round face and balding pate became the flavor of the season.

“After ‘Sideways,’ people saw me in a very different way. They saw me as a guy who could handle bigger parts and more diverse things, a guy who wasn’t necessarily comedic. It changed everything. More people recognized me, and I didn’t like it very much at first. I’m fine with it now. I find a kind of pleasure in it now because people are generally very nice. It’s interesting because I get to meet people. I look at it that way.”

This latter-day fame was a long time coming. And Giamatti proves the wisdom of that status as the relentless U.S. attorney in hot pursuit of a hedge-fund mogul (Damian Lewis) in Showtime’s “Billions,” premiering Jan. 17.

As the veteran of critical hits like TV’s “John Adams,” (for which he won an Emmy) “Straight Outta Compton,” “The Illusionist” and “American Splendor,” it’s hard to imagine Giamatti on the acting ropes.

But there was a time. “There was a period around when my kid was born I was working pretty steadily and it was great, and was doing a lot of theater. Then there was about a two-year period, I worked, but not very much. I couldn’t get ANY theater jobs. Everything just dried up for about two years. I could work but it was really, really stretching it from about 2001 to 2003, 2004.”

If DNA had its way, Giamatti would be a teacher. Three of his grandparents were teachers, his dad was a professor of English Renaissance literature at Yale, his mom a teacher.

But as the alumnus of a private boarding school, (he didn’t board) he lacked the academic zeal, he says.

“I was on the swimming team and one day I went by where they were holding (play) auditions in the classroom, and I was listening. This girl said to me, ‘You’re really funny, you ought to go do that.’ So I just went in and got a part in it. It’s a weird play, not a good play. So I did that, and I remember being thunderstruck by this thing.”

After graduating college, with an English major, he headed for Seattle, with no idea what he was going to do. His dad died just before he left. “I felt suddenly like I needed to get off my a— and do something with myself … I did start making money as an actor and went back to school for it and thought, ‘This is what I’m going to do.’ I got more serious than I’d ever been about anything.”

He returned to New Haven and earned his master’s in drama from Yale. “I never thought too much about being famous,” says Giamatti, who’s nattily dressed in a blue-gray suit, a blue and white dress shirt and tie.

“I wanted to do good work and wanted to work all the time and … I had a funny notion that I’d be able to do that without being famous particularly. I don’t think any actor could say the desire to be recognized wasn’t in there somewhere. But famous? I still don’t have a desire for that.

He’s been married for 18 years to Elizabeth, whom he met when she was serving as dramaturge on one of his plays. They have a 14-year-old son whom Giamatti describes as “very smart and bookish and interested in stuff like that.”

As for him, the actor admits that he’s overly self-critical when it comes to his work.

“I’m haunted by things I did in movies years ago. I say, ‘Why did I do that? Why didn’t I do something different? Why didn’t I do what I thought of five minutes after we finished shooting a scene?’ I don’t even know if it’s perfectionism. I wish it were perfectionism then I would insist on getting it right. But a lot of time I go, ‘It’s OK, OK,’ and go on feeling I never got it right.”