Marching through the streets of Alexandria yesterday on the last leg of a civil rights protest that started in Alabama and will end Wednesday in Washington, Harrison Nash said he realized that 1982 is not the 1960s.

The 37-year-old Nash recalled that when he marched triumphantly into a big city during the protests of the '60s, local blacks would join in the march, picking up the protest slogans along the way. Everyone seemed "fired up" in those days, just waiting for the chance to show their anger at racial discrimination. Yesterday, things just weren't the same for Harrison Nash.

Only about 30 people joined the 60 or so men who have made the Southern Christian Leadership Conference's "Pilgrimage to Washington" to lobby for the extension of the Voting Rights Act, which both the Senate and the House have now passed, and to protest the high unemployment of blacks and President Reagan's budget cuts.

"We were really expecting a lot of people in Charleston, S.C., when we had Martin Luther King III speak at our rally," Nash said. "But you know it was very shocking, even with Martin Luther King's son, people still wouldn't show up.

"In big cities people have gotten to think that there is nothing wrong," Nash said. "People in urban areas think they've arrived, and they are very content with the way things are."

But Nash said he still was happy with the way the march turned out. He said that in the South the group had added 50,000 blacks to voter registration lists. And though people in larger cities such as Alexandria seemed indifferent, in small towns the group's rallies packed churches, Nash said.

The Rev. Joseph Lowery, president of SCLC, called the poor turnout in cities acquiescence to racism.

"For the urban people integration doesn't exist anymore and that has tended to calm people," Nash said. "Out in less-developed rural areas people can still see racism and that seems to be why more will turn out for our protest. Pseudo-integration seems to have instilled some apathy in city people."

Nash's wife, Janice, 23, who took part in the march even though she is two months pregnant, said the apathy she had seen worried her. "Struggles like we have been through are still not over--just pacified for a few years," she said. "Even with the passage of the Voting Rights Act, our voting rights are still not secure--where is the permanence in that, where is the permanence for my children?"