DR. BENJAMIN SPOCK, the baby doctor and the antiwar activist, walked out of the White House Tuesday holding the hand of his wife and stepped over a chain. He was, if truth be known, a trifle nervous, but he walked onto the driveway where the public is not allowed and sat down to pray and wait, as he has so many times before, to get arrested. I tell you this because almost no one noticed.

Inside the White House, business went on as usual. The lpress corps did not come to see Spock get arrested and the tourists who asked what was happening, could not have cared less when told that Benjamin Spock and 11 other protesters were sitting in the White House drive waiting to be arrested to protest the budget cuts.

In the papers, there was a very small item about the arrest and on the television I saw there was nothing about the incident and soon, I know, Spock will be in Maine where he summers, on his boat, actually, having spent his de rigueur one night in jail, making it the eighth or ninth or maybe tenth night in his 78 years that he has spent behind bars. For this an ungrateful nation gives him a fat yawn.

Benjamin Spock is thought to be a throwback to the '60s, the Harold Stassen of something called The Movement. He is thought to be strangely out of joint, lost the rhythm, does what he used to do when the reasons for doing it are gone. There is no war, Doc, and the Russians will not join SANE and the country has moved to the Right. The president is a Big Man on Campus, a charmer who once made Spock's generation of children his foil. He took them on at Berkeley and spanked them good -- spanked them, Doc, and they either loved him or hated him for it, but they got the point.

Spock has heard all this. He sat in the bleachers behind the White House with the other tourists, waiting for his tour group to be called, answering the why-are-you-still-doing-this questions of an occasional reporter. He talked with the tourists, some of whom know him, some of whom have been raised by his dictates. "You've revised your book," says one woman.

"Just the techniques," he says. "Not the philosophy."

Spock is not by upbringing a rebel. He was a New Yorker who summered in Maine and rowed at Yale. He believes in decorum anbd propriety, in doing things the right way, unless, of course, there is no choice but to do them the wrong way. The Reagan budget, he says, has forced him to make that choice. Civil disobedience convinces people you are serious and the Reagan budget, Spock thinks, is seriour business.

"The kids will suffer," he says.

It's still the kids.

And it's still really the same fundamental issue -- the welfare of children. He says it was a concern for kids that got him into politics in the first place -- nuclear disarmament at first. Then the war, then nuclear power and now the Reagan budget and what it will do to the health and education of kids. He knows, of course, that he is out of step, but he has been out of step before and the country has after a while picked up on his beat. He thinks it will happen again. It takes time, he says, but it will happen. A man does not go from hero to fool because someone wins an election and the country adopts, like a coat off the rack, a new philosophy. Maybe more people would have come to see Spock if he was advertised not as someone willing to risk arrest, but as that rarest of all human commodities -- someone who will not change his beliefs to suit the times.

As quickly as he could, Spock moved through the public rooms of the White House. He said very little and then, almost unexpectedly, the tour was over and he was out on the porch and walking down the driveway. His group watched him. He walked a bit and then, for some reason, picked a spot and threw a long leg over the chain. He was on the driveway and the others followed and then they all joined hands and sat down and prayed.

Benjamin Spock was arrested. Few people noticed. The White House shrugged. Benjamin Spock spent yet another night in jail. The nation was asleep. It was a joke. On him, maybe. On us, certainly. But Benjamin Spock would say the issue was not us or him, it was poor kids. We'll wake up when we hear them cry.