James Brannon, 51, an Ohio iron worker unemployed for the past year, came to Washington yesterday to tell his congressman that he needed a job.

When he arrived at the office of Rep. Dennis E. Eckart (D-Ohio), Brannon said a legislative aide told him that Eckart was not available, but was doing all he could to help.

"I told him that I'm unemployed and my wife is unemployed and please ask the congressman to do more," Brannon said.

After leaving Eckart's office, Brannon, of Cleveland, joined several thousand other unemployed people from across the country in a rally to demonstrate their frustration at not being able to find work. U.S. Capitol Police estimated that 2,000 people participated in the rally at the West Front of the Capitol.

The rally was part of a day-long lobbying effort organized by the National Unemployment Network, a non-profit lobbying group for unemployed workers.

Its goal was to urge lawmakers to pass legislation to create more jobs, end foreclosures and evictions of unemployed people, and to extend unemployment benefits. Groups participating in the event included the United Auto Workers Union, the National Council of Churches, and the Full Employment Action Council, a national coalition of civil rights, labor, church and public interest organizations.

Rep. John Conyers (D-Mich.) told the crowd that President Reagan should be impeached and House Speaker Thomas P. O'Neill Jr. should give up his leadership post for failing to deal with joblessness. "Why don't we impeach Reagan for incompetence," Conyers said, drawing loud applause from the crowd.

Conyers said later that if enough people demand Reagan's impeachment, he would lead the effort in Congress.

Throughout the 90-minute rally, many demonstrators, dressed for the warm, sunny weather in shirt sleeves and windbreakers, held up signs that read: "I Need a Job," "I Want My Job Back," and "Put Reagan in the Unemployment Line--Vote Democratic."

While the out-of-town demonstrators met with their congressmen to try to change public policy, some of the District's unemployed were standing in line on Sixth Street NW, trying to get free butter.

Lee Sledge, 31, who said he was laid off his job as a maintenance worker on Feb. 28, was one of those in the line that wound through the First Rising Mt. Zion Baptist Church at 1240 Sixth St. NW. The butter was distributed by the Department of Agriculture as part of a continuing program.

"Anybody who says that I don't want to work is a liar," said Sledge, who has worked as a construction worker. "I want things out of life and I can't get it like this. I'm used to getting up at 5 a.m. to go to work. Being unemployed is boring as hell."