Evoked for a few moments here last week was some of that '60s optimism that poor people can make a major contribution toward solving the seemingly intractable problems of youth crime, unemployment and deterioration in big cities.

At times, the discussions sounded like a reunion of veterans of the war on poverty. But the two-day conference, which asked, "Urban Crisis: Can Grassroots Groups Succeed Where Government Has Failed?" was put on by the American Enterprise Institute, the conservative Washington think tank and brain trust.

The conference featured neighborhood activists who work with youth gangs in Philadelphia, Puerto Rico and Los Angeles, train unemployed adults in Hawaii to become business people and spearhead successful efforts to rebuild and renovate a blighted neighborhood in St. Louis.

A couple of White House aides stopped by briefly to report President Reagan's enthusiasm for the idea that citizens can deal effectively with the problems facing them.

Coincidentally, elsewhere in town, a modest demonstration of other community activists and other poor people declared one of the days the conference met a "National Day of Mourning," and marched from the White House to the Capitol in vain effort to get Congress to oppose Reagan's plans for chopping or dismantling an array of federal urban and social programs.

At the American Enterprise Institute's meeting, discussions avoided highlighting the problems caused by federal budget cuts but accented instead the obstacles government often throws in the path of the grassroots community groups.

American businessmen may have their problems with the Occupational Safety and Health Administration but many of their tales of horror pale by comparison to some of the stories told by Sister Falaka Fattah. Sister Fattah and her husband have taken more than 500 poor and troubled youth into her House of Umoja in Philadelphia over the last decade and worked to channel their anger and restless energy into positive pursuits.

Government inspectors once tried to get Sister Fattah, a gracious woman of quiet strength who wears colorful headwraps and flowing African dresses, to fire her husband. They rarely saw him around the office and assumed that his role must be minor. In fact, she said, he spends his time out on the corner talking to youth in street gangs and making the efforts, for which the House of Umoja has won acclaim, to put a stop to Philadelphia's legendary gang wars.

Macler Shepard, a friendly and gregarious former numbers operative in the north St. Louis ghetto who unexpectedly found himself the leader of a neighborhood group protesting urban renewal plans, had similar stories to tell and similar successes to report. In his blighted neighborhood near where the notorious Pruitt-Igoe public housing project stood before it was blown up after becoming one of the federal government's spectacular failures in providing decent housing for the poor, his group has successfully promoted efforts to renovate hundreds of houses and bring in new firms and businesses.

The successes of these and other groups, especially their ability to overcome the barriers erected by government itself, were applauded by white conservatives.

White House senior policy adviser John McClaughry read to the conference portions of a radio commentary Reagan had delivered four years ago on the same subject.

"If the dead hand of government can be lifted -- or ignored -- groups of citizens can and will come together to deal effectively with problems facing them," Reagan had said. "The key is in devising a system in which power and responsibility are dispersed at the grassroots, instead of being concentrated in a hierarchy of bureaucracies and institutions."

Ron Baker, a white Dayton businessman and member of the American Enterprise Institute's neighborhood revitalization project advisory council, declared himself to be ecstatic at hearing the emphasis on self-reliance and hard work from the largely black neighborhood groups.

"I think so many of the private sector have the wrong image of what the colored people want," Baker told the conference. Later, he said with enthusiasm he thought he would have little trouble getting businessmen in Dayton to make big contributions to aid projects like the one run by Sister Fattah.

Conservatives' discovery of community activists and their self-help efforts must bring a sense of mild satisfaction to those Kennedy- and Johnson-era policymakers who had written into the Economic Opportunity Act of 1967 that the war on poverty be waged with the "maximum feasible participation" of the poor.

Where the Great Society went wrong, argues Robert Woodson, the American Enterprise Institute's only black resident fellow and the organizer of the conference, was in the government's naive belief that it could create grassroots community action agencies and model cities programs and "parachute" into poor neighborhoods centrally designed programs for them to implement.

Too often ignored, Woodson said at the conference and in his recently published book, A Summons to Life: Mediating Structures and the Prevention of Youth Crime, are the enduring institutions in black communities. These include the churches, lodges and fraternal organizations and the corener barbership to which people most often turn for help in times of crisis.

Woodson rejects both the conservative panacea of more police to solve the problems of rising crime and the call of liberals for more social programs. He believes the answers can be found in indigenous groups like Sister Fattah's House of Umoja.

He says that her efforts cannot be duplicated in other cities, that the solution is to foster the emergence of other indigenous groups in other communities with styles of operation best suited to their own neighborhoods.

Just how this can be done was not answered during the conference. Nor was the impact of Reagan's program of "economic recovery" fully explored.

Most of the featured groups got started without federal aid and appear to have survived both the '60s and the "Me Decade" that followed, not only because of their longstanding ties in their communities but also because they seem to have always kept a firm vision of what they wanted to achieve. They were not afraid to turn down government funding if the dictates of a federal program conflicted with their own sense of their goals. Sister Fattah did not fire her husband.

And unlike other fallen Great Society efforts -- Washington's Pride Inc. for example -- they resisted the lure of new grants to expand when they did not believe they were ready to do so.

But they have made good use of government funds from a variety of programs for jobs training, housing rehabilitation and urban economic development and there was muted concern among the activists about the administration's plans for cutting them. So, the question remains to be answered as to whether last week's meeting will a year from now be looked on as the beginning of a new alliance between activists and Reagan conservatives or whether the groups at the conference will remember it, like the groups demonstrating at the White House and Capitol, as a "National Day of Mourning."