The meeting room was small, but then so was the crowd as the Leadership Conference on Civil Rights opened a two-day meeting yesterday in what its chairman came close to describing as the worst of times for the liberal organization.

"This is a delighful turnout," chairman Clarence M. Mitchell Jr. told some 100 people of the Washington Hilton, "especially when one considers the times in which we live and the circumstances in which we operate."

If Mitchell had intended to set a slightly defensive tone for the conference's 31st annual meeting, he succeeded brilliantly. Both the featured speakers, House Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.) and Sen. Charles McC. Mathias Jr. (R.Md.), warned of a difficult task the organization and its allies face in preserving civil rights gains made in the 1960s and '70s.

Rodino referred several times to what happened "last night," by which he meant President Reagan's triumphant return to public activity Tuesday in his nationally televised speech to a joint session of Congress and the enthusiastic response be received on Capitol Hill.

Judging by the mood of Congress and the impact of the speech, Reagan is likely to get most of the budget reductions he is seeking. Rodino said.It is the job of liberals to preserve spending for essential programs and fight attempts to dismantle civil rights and other liberal legislation.

But, Rodino said, "it is tremendously important that we recognize that the climate is a lot different.

"That is the understatement of the day," he added as the audience laughed.

The Leadership Confeence on Civil Rights has made an extension of the voting Rights Act of 1965 its top legislative priority. A House subcommittee is scheduled to begin hearings next week, and Rodino said he believe there is wide bipartisan support in the House to extend the law.

But Rodino said that in the Senate -- now controlled by the Republicans, with a southern conservative, Storm Thurmond (S.C.), heading the Judiciary Committee -- there will be more opposition. And if the law is not extended for 10 years, Rodino said, "we will be in a difficult position and there will be an effort to negate the gains that have been made."

The changed makeup of the Senate poses a problem on other issues as well, Rodino said. Last year, be recalled, a Carter administration measure to strengthen federal fair-housing laws cleared the House but died in the Senate. Senate opposition to strengthened fair-housing laws is even stronger now, Rodino said.

On these and other measures, but said, the conference and other liberal organizations need to generate the kind of grass-roots popular support they enjoyed during the 1960s when a series of liberal laws were enacted. He warned that without such popular support "it is going to be, if not impossible, very difficult to achieves these objectives."

Mathias also warned that supporters of the Voting Rights Acts face "a tough fight" in winning its extension. He said that there have been many interpretations of what Reagan's election meant but that he was certain it was not a mandate "to repeal the Voting Rights Act of 1965" or to roll back "the whole social agenda that all of us have worked on for the last 20 years."

That seemed to be the attitude of others at the meeting, who said they recognized that the president's economic program is the focus of attention now, pushing such issues as the extension of the Voting Rights Act into the background, at least temporarily.

"The budget has become an all-consuming game," said Jane O'Grady, a conference official. "We will just have to suffer with that for a while."