A huge roar went up from 15,000 people gathered under the cold night sky as the leader of Poland's independent unions, Lech Walesa, stepped on the stage of an open-air theater here. Warmed by the glare of television arc lights, he raised his arms in the clenched-fist gesture of triumph that has become familiar to millions of Poles in the last three months.

After a rousing speech by a hero of Poland's wartime resistance ("We are witnessing the birth of a movement unique in the history of the world"), Walesa answered written questions from the audience. They were brought up to him by an honor guard of merchant seamen in smart blue uniforms.

Practically all the questions were political in tone. Some called for retribution against politicians responsible for the crisis ("Sentence them to death," one elderly woman shouted). Others asked when the independent trade union federation Solidarity would set itself up as a political party to rival the Communists.

There was mention, too, of the murder during World War II of 4,000 Polish officers at Katyn -- a massacre attributed by most Poles to the Soviets but blamed by official history books on the Nazis.

Walesa handled these potentially explosive subjects with wit and skill. He joked that there were not enough prisons to hold all of Poland's corrupt officials.

"We don't want to put these tycoons in jail, as then they'd just be getting fatter at our expense. Instead, they should hand over their stolen villas and bank accounts to us -- and we'll distribute them among the people."

Walesa went on, however, to remind his audience that Solidarity was a trade union -- and there were some sensitive areas in which it should not meddle.

"We cannot solve all problems at one; we must get ourselves organized and proceed step by step. If we were to become a political party, he said, implicitly acknowledging the limits to Soviet tolerance of pluralism in Poland, "that would lead to diseaster."

The recent meeting in Szczecin, the drab Baltic port that was one of the leading strike centers in August, reflected some of the dilemmas facing Walesa and Solidarity.

Now fully recognized as a legal organization, the communist world's first independent labor union has come in from the cold.Walesa would like to concentrate on organizing the union more efficiently, giving the authorities time to introduce reforms. But he is under tremendous pressure from his supporters, who after years of political repression and economic frustration, want changes immediately.

The speed with which Solidarity has grown and consolidated its position since the strikes is remarkable. Once the dream of a small band of activists, Poland's independent union movement has between 8 million and 10 million members out of a total population of 35 million. Its industrial muscle has forced the resignation of a regional governor and can send ministers scurrying about the country from one pay dispute to another.

Nevertheless, despite its recent legal registration, Solidarity still has not been integrated into the mainstream of Polish politics. Its power rests solely on its ability to order its members out on strike. At times the union seems fated to eternal opposition, enjoying great popularity as a rival power center to the ruling Communist Party but never itself grappling with Poland's desperate problems.

This state of affairs is partly a product of the party's insistence that it should retain a monopoly of political power. But it also reflects the determination of Solidarity's more radical leaders that their revolutionary purity must not be sullied by getting too close to the government.

Complicating the government's attempts to win Solidarity's confidence is the grave economic crisis. Long lines form for most basic foodstuffs, from potatoes to meat or bread. Even candy is difficult to obtain -- as it is being used as a substitute for sugar. Already deeply in debt to the West, the Polish authorities do not have the reserves to buy themselves political breathing space.

Last summer's successful strikes, far from diminishing the worker's sense of injustice, have triggered off a new series of demands. Individual groups of workers have pressed their cases by bringing blankets and occupying administrative offices until the government negotiates with them.

A more recent development is Solidarity's attempts to oust government officials and factory managers whom it regards as opponents. In Czestechowa, in southern Poland, the provincial governor and several of his associates were forced to resign as a result of union pressure. In addition, at least one Solidarity branch has demanded the dismissal of Warsaw's newly appointed Communist Party chief because of his alleged involvement in the killings of workers during riots along the Baltic Coast 10 years ago.

This constant attrition is wearing down the authorities' nerves. A senior official complained recently that the government was running out of deputy prime ministers to take part in negotiations.

Walesa seems torn by a wish to help the government out of its difficulties and a sense of obligation to his supporters. At a recent meeting of Solidarity's national committee, he argued passionately that it was necessary to put some order and discipline into the process of wage bargaining. Organizing independent unions -- and not seeking higher pay -- was the first priority. Yet a few minutes later, he was speaking equally passionately on behalf of the underpaid.

The conflict in Walesa's mind is echoed by divisions within Solidarity itself. A delegate from Wroclaw told the national committee that it was useless to strike for higher pay when the money paid out was just paper. "We are striking against each other, trying to grab our share of the decreasing amount of goods available on the market," he said. "The government is just laughing at us."

On the other hand, Andrzej Gwiazda, one of the founders of the independent trade union movement in Poland, argued that constant struggle with the authorities was the best way for the union to organize. He pointed out that so far no negotiations with the government had succeeded unless accompanied by a strike or the threat of strike.

Despite Walesa's effort to calm emotions, senior Communist Party officials are worried by what they regard as a dangerous wave of political demagoguery released by Solidarity's activities.

The party's fears were voiced in a recent speech by Miecyslaw Rakowski, the influential editor of the weekly magazine Polytika.

Rakowski reportedly said hopes of social peace in Poland resulting from the Gdansk agreement establishing independent trade unions had not been realized so far.

"The crisis continues to worsen; one has to realize that," he said. Predicting possible "further complications," he said he worried that hard-line elements in Solidarity were getting the upper hand.