"It was like any character, you know," said Ed Harris.

In one spectacular leap, the actor jumped from obscurity to stardom by playing John Glenn in "The Right Stuff," the blockbuster epic about the space program. In a single day two weeks ago, there he was--in socko red, white and blue--on the Newsweek cover and in the right-hand corner of Time's cover as well. It was instant celebrity for Harris at 32.

"I'm just grateful that I am far away from it all down here in Waxahachie," he said. His current project is a film about Texas during the Depression, costarring Sally Field. "It really worries me how I would have taken it all if I had been in L.A.," he declared, sitting by the pool of the Brookside Inn in this placid little town (population 14,624 and less than an hour from downtown Big D on the interstate). It was four days after the twin covers had hit the stands.

"Sure, I knew the movie would be big," Harris continued. "But it really never occurred to me that this," gesturing at Newsweek, "might have happened. I hadn't given much thought to being on the cover of anything. Maybe all seven of us would have made a cover the actors who play the seven Mercury astronauts , but not me out there alone. Never."

Granted, it wasn't just Harris' extravagantly hailed performance that brought him this bonanza. John Glenn is running for president. So far the senator has kept his distance from it--not even planning to attend tomorrow's gala American Film Institute benefit opening at the Kennedy Center. But Glenn said at a recent Democratic fundraiser here that he had returned a call from Harris and gotten a busy signal, adding, "I'm looking forward to meeting him."

Back in late 1981 when Harris auditioned to play Glenn, the part's full potential to enhance his career--because of its political implication--was not clear.

"They asked me to read for Glenn. They weren't interested in me reading for anyone else. I wanted to do it just because I wanted to be part of a good film. I had my work cut out for me.

"I actually auditioned twice. The first time I read it was just in an office with producer Bob Chartoff and director Phil Kaufman. They wanted me to do the press conference scene, the first time the astronauts were introduced before the public. And I didn't do a very good job. Phil kept asking me to smile more, you know. And be more gregarious, and there's nothing like trying to smile when you're nervous. You know what kind of smile that is. And I left and didn't hear anything about it.

"Then in about a month there was another call. So I went back in again and they videotaped it. And it was a little more intimate a situation. It went better. But Phil insists that I hit the wall with my fist when I went out, because I was still a little pissed off about my performance."

Later there was a call from Harris' agent, who said that he got the part. "They're not giving you any money but I want you to do it anyway," he said his agent told him.

"By the time 'The Right Stuff' was finished--about a year ago--I was kind of aware that it might have some political impact or at least be talked about. But during the first five months of shooting, there was just speculation that Glenn might be interested in running. I guess Kennedy announced he was not running somewhere in there."

His career in the movies was slowly developing, but he had not hit it big (among the movies: "Borderline," "Creepshow," "Knightriders," "Swing Shift" and the about-to-be-released "Under Fire").

He denied published reports that he made himself up to look as much as possible like Glenn at the auditions.

"I don't know where people got that," he protested. "I didn't put on any freckles and I had short hair to begin with."

But it takes only one glance to see that, in many ways, Harris looks remarkably like Glenn. The hair color is the same--and both are balding in the same way; they are approximately the same height, and both have ruddy complexions. Harris' jaw and chin are square, like Glenn's, but are narrower. Both have wide grins. Harris even has Glenn's squint.

Harris' dominant facial features are his eyes, which are deep and penetrating. And he is almost a decade younger than the senator was when he orbited the earth in Friendship 7.

Another Glenn-like trait is Harris' slightly flat, soft voice--a blend of spending half his life in Tenafly, N.J., his birthplace, and the other half in the West. "I've worked hard at shedding the Jersey accent," he said, " 'dese' and 'dose' and so on." They return automatically, he granted, "when I get riled. But that's one of things about playing Glenn. He's from Ohio, and he sounds like it. I didn't want him to sound like Jersey."

Harris' manner also seems right for the part--unassuming and earnest, with quiet flashes of humor.

There is also apparently a touch of a daredevil cutup in Harris--not inappropriate in a movie about test pilots and astronauts. He was asked if he precipitated one of the most anxious moments in the shooting of the film, when he so thoroughly mangled his face in a rowdy moment that all the miracles of modern makeup would not entirely hide it.

"I'll keep that secret." Pause. Grin. "Well, you see, I was skateboarding on a luggage rack . . . it just happened to go off the curb . . . it was a Holiday Inn."

Any further details? "Let's leave it at dat," he said, the Jersey accent temporarily restored.

"They really didn't give us fast cars for us to drive on the set--not that Glenn was one of the guys who would drive fast cars." (Harris drives "a cheap pickup" and in Waxahachie he was riding around on a decrepit old bike.)

Is he married? "No . . . but maybe soon." To whom? And he goes off the record for the only time in the interview.

Will he pose with a copy of Newsweek? "I'm sorry. But I just don't wanna. It just seems weird to me. Okay? All right?"

Harris has had considerable stage experience on the West Coast, many of them heavy roles. "I like to do things that arouse people's emotions, I guess, characters that have something at stake, I guess." The actor he respects most: Robert Duvall (who also filmed "Tender Mercies" in Waxahachie).

Earlier this year Harris made his New York debut at the Circle Rep in playwright-poet-actor Sam Shepard's new play, "Fool for Love," to much praise. The character was a passionate, lusty rodeo rider. Glenn is almost the opposite. "He's very contained," said Harris. "I knew that I just couldn't be in any way flamboyant and do it right. The drama in the man comes from his belief system, and how strong that is. So I tried to make that the core of the guy. What he stood for, in the face of everything else."

Some critics have said Harris makes Glenn a more sympathetic figure than Tom Wolfe's book "The Right Stuff," on which the movie is based, where he is characterized as a bit rigid and preachy. Asked if he deliberately made Glenn a less sanctimonious character, Harris replied: "Well, I hope so. I mean, I think Wolfe had a point of view about Glenn, had certain judgments about his character. And I think when you see him portrayed, then you see him get a chance to explain why he does what he does. I mean, you see him in action, not reading what somebody has written about him."

What about the famous locker room scene in which Glenn warns the other astronauts about the need to set good personal examples for the sake of the Project Mercury?

"I hope that sounds like he said, 'Look, we are responsible for this whole program.' He was not telling anyone not to do anything; he was telling them to be careful in what they did, because the program is very important and let's not blow it."

He is asked what he would do if he were approached to play a direct role in the presidential campaign.

"I've thought about it," he said. "I consider myself a fairly political person, but in this situation I'm sort of lying low. I don't feel like committing myself and I'm not going to at the moment. The last time I registered, I think I registered as an independent. I don't like saying these things. I see myself as an actor, and that's what I love to do. And some actors have taken strong political positions, and I approve. But I just don't think I am educated enough politically to take a stand that strong right now."