David Byrne loves America. He knows she has a reputation, but he still desires her. She leads him on, then she walks all over him. But still he comes back for more.

At any rate, that's the way he told it in "Miss America", his criminally overlooked single of last year. "Oh, Supergirl, I'll be your Dirty Harry," he sang adoringly, as she ground a heel on his hand. Latin rhythms played, in a grotesque parody of Bernstein and Sondheim's "America". His country's pants dropped round her ankles. Still, he wanted her. "Since I've travelled in Latin America, I know that love-hate relationship is common," he sighs. "America has brought wonderful things to the world. But it's nasty and oppressive, too."

When he was with his band Talking Heads, commonly dubbed "the best band in America" in the Eighties, David Byrne's strained, sometimes psychotic voice left little time for such considerations. One of the original punk bands, coming out of New York alongside Patti Smith and The Ramones, Talking Heads looked, someone noted, "like emotionally disturbed preppies". The image of a man so buttoned up he could barely breathe, so wired he could hardly stand still, was increased by Byrne's performance in the concert film Stop Making Sense, and has been repeated by every journalist who's met him.

Over the phone wires from a Leeds hotel, midway through a brief British tour, it's impossible to say if those things are true. Perhaps, when no one's watching, he doesn't have to twitch. His voice is certainly less freakish than it is usually portrayed. Its only oddity is that it strains when he says words that move him. The first words that make his voice crack are "Elvis" and "Presley". Byrne may once have looked like a preppie but, in his heart and head, it's honky-tonk America that he's loved since he was a child, his country's rough sense of possibility. "I was always aware of the mad, exuberant creativity out there," he remembers, "whether it was from Elvis or the Beat writers or artists, or country and western musicians."

It was only when he was older that Byrne saw the danger in such openness, such belief that anything was possible. It's this mess of love and fear that defines his country for him now. On his latest album, Feelings, he sings, "The terrorists are acting out of love, sweet love", and sounds like he loves them too. He means the people who bombed Oklahoma City. "I think serial killers and the Unabomber are the other side of the coin of the generosity and the creative spirit that's in America," he says. "The sense of can-do, that all things are possible, unrestrained by a class system or race or religion. Which is all a lie." His voice strains. "But it's there to some extent, and it's believed to a great extent. I think that creative urge, when it fails and becomes directionless, manifests itself in Unabombers. The fact that I see that the two go hand in hand is a slightly unusual viewpoint in America. Most of the time, people think that, if you stamp out the bad men, if you just say no, it'll be all right."

What does he mean when he says the terrorists are acting out of love? What does it mean about America that its own citizens can kill for love of it? "I think it means that they feel helpless," he says with feeling. "That they feel a lack of connection, and a lack of access to channels, to ways to express themselves. Freedom is a deception, if you don't have access to those things." Does he think the Oklahoma bomb was a cry of frustration? "Yeah. Granted it's some lunatic. But the lunatics might just be ultra-sensitive. They're the ones who've snapped first."

It isn't only Byrne's relationship with his country that is ambiguous. His songs in recent times seem to express frustration with his skin, a wish to escape it. Is that really how he feels? "Oh, yeah. I think music does that, that's part of the excitement of music. It used to be more evident that here was this person who did not belong on stage, but had to get on stage in order to complete himself. That something was missing, and I found it on stage."

He sings, on Feelings, of love letting him forget himself. Is that a good thing? "Yeah. I think it's great. It doesn't have to be a permanent condition, but it's the kind of thing that happens on a dancefloor, or when people go to church, or at football games. Just knowing that that can happen to you is a great feeling." Knowing there's some hope of release? "That there's some hope of being different."

Many still see Byrne as a Talking Head, however he sees himself. He's touchingly modest about this, and people's unwillingness to give Feelings, an album as good as anything he's ever done, a chance. His model for a working life isn't a rock star, anyway, but the owner of an Austin cafe he used to frequent, a woman whose sense of pride rubbed off on everyone she met. "This woman had imparted a sense of possibility to people," he says, "and they took it with them. It was very inspiring. It seems like the counterweight to all the horrible shit you read in the papers every day is the weight of all the tiny people doing little, kind things once in a while."

It was those people and those acts that Byrne caught in his best songs in his old band, and in a film he made, True Stories. But he seems to have more trouble doing it now. On Feelings, you can hear dignity and happiness in the music. But in the words, it seems barely possible. "I think maybe I need to get out of the States," Byrne says abruptly. "Wherever you go, you're going to be aware of what's going on. But in America you get this glare of the media, you're bombarded with everything being for sale. It's a very surreal universe. It can completely obscure anything else."

Does he think it has dimmed his sense of decency? "Yeah, I think it's been drowned out by the din of all that other noise. It's still there. But, in America, it's harder to hear."

David Byrne: Cambridge Corn Exchange tonight (01223 357851), Shepherd's Bush Empire tomorrow (0181-740 7474). Feelings is released on WarnerBrothers' Luaka Bop label.