WARSAW, DEC. 8 -- Poles will choose their first popularly elected president Sunday in an atmosphere of high drama unusual even by the standards of this tumultuous nation.

Although Solidarity leader Lech Walesa is the overwhelming favorite, observers say they cannot rule out an upset by challenger Stanislaw Tyminski, who has promised that ordinary Poles can be millionaires within months if he is elected.

Government and independent voter surveys show Walesa, the 1983 Nobel Peace Prize winner, with an overwhelming lead of more than 50 percentage points over dark-horse candidate Tyminski, the emigre businessman whom Walesa calls "the man from Mars" and a front man for Poland's ousted Communist rulers.

But pollsters, newspapers and voters say those numbers may be unreliable and that a Walesa victory could be in doubt if voter turnout is low. The private polling organization Demoskop predicted Friday that Walesa would be "in danger" if voter turnout -- 60 percent in the first round of voting, held Nov. 25 -- falls below 40 percent on Sunday.

"It's roulette. You can't predict it," said Krzysztof Majkowski, a farm co-op manager. He echoed government and private pollsters who said Friday that they believed many Tyminski supporters had lied about their intentions.

"All of the polls could be wrong," said the state television polling organization. "It can be assumed that some Tyminski supporters are afraid to reveal their real preference" because of social pressure to vote for Walesa.

Tyminski, a native Pole who returned here to run for president after living for 21 years in Peru and Canada, astonished Poland's political establishment by winning nearly a quarter of the votes in the first round. He finished well ahead of Solidarity Prime Minister Tadeusz Mazowiecki, forcing Walesa into a runoff, prompting Mazowiecki to resign and bringing the strife-ridden Solidarity movement to the realization that splits within the organization could result in a Tyminski victory. Mazowiecki has since thrown his support behind Walesa.

Many Poles were embarrassed that a virtual unknown could beguile 4 million voters with promises of easy wealth. Others saw the first-round result as a disturbing sign of Poland's immature political culture, little more than one year after legislative elections wrested power from the Communist government that had ruled for more than 40 years.

Opinion polls indicate Tyminski's 23 percent share of the vote has declined to about 16 since the first round. He is thought to have been hurt by two weeks of ugly, chaotic campaigning and an endorsement for Walesa by Poland's Roman Catholic bishops.

Whether Tyminski wins or loses on Sunday, many view his presence on the ballot as a threat to Poland's emerging democratic institutions and its free-market economic reform program, the most rigorous and successful in Eastern Europe. The leaders of those nations can be expected to view the outcome of Poland's election largely as a referendum on its reforms.

In his campaign appearances, Tyminski denounced the reforms as a World Bank conspiracy to impoverish Poland. He offered voters a vague "democracy of money" where all could become rich, as he had in the West. He accused Walesa of wanting to sell Poland out to foreigners and reassured workers worried about unemployment by pledging that he would not privatize "healthy" state-owned industries.

Some analysts warn that a Tyminski victory could reverberate across post-Communist Europe, where new democratic governments are threatened by popular dissatisfaction over falling living standards and rising unemployment.

Walesa has called Tyminski a "con man," and his candidacy "humiliating" for Poland. Others see the 4 million votes cast for Tyminski and his seemingly unrealistic campaign promises as proof that Poles are less convinced of the necessity of economic hardship than had been assumed.

Despite two weeks of damaging revelations in the Polish press and a campaign that in its final days degenerated into chaos, Tyminski's promises of quick, painless riches appeared to retain their appeal to his supporters in small towns and rural areas.

Tyminski's rags-to-riches story, his philosophy -- a blend of Dale Carnegie-esque positive thinking and New Age mysticism -- and his sheer novelty remain attractive to villagers who resent Poland's old Communist and new Solidarity establishments.

"Last time they said they supported Mazowiecki and voted for Tyminski," said Majkowski, who manages the largest farm co-op in the northern region of Olsztyn, where Tyminski outpolled both Walesa and Mazowiecki in the first round.

"This time they say they'll choose Walesa, because the climate is that one should vote for Walesa. But deep inside, they're not convinced," Majkowski said. "They see someone who left Poland and made money, and they think that this sounds good."

Tyminski has several former secret police officers on his campaign staff, and it is expected that he will draw many of the more than 1 million votes cast in the first round for the Communist Party candidate.

"Many people are afraid of Walesa's 'ax,' " said Aleksandr Bochenski, a farmer and councilman in the town of Barczewo, referring to Walesa's pledge to hack away the former Communists remaining in Poland's government. "They are afraid of a settling of accounts. They will vote for Tyminski to create disorder, because they don't want to lose their positions and to keep others from looking too closely at their pasts."

But Tyminski's support as measured by opinion polls began to nosedive this week after a televised press conference in which he claimed to have documents that incriminated Walesa. He refused Walesa's demand to make the alleged evidence public.

Tyminski's colorful but murky past in Canada and the Peruvian jungle and his bizarre personal style became an increasing source of ridicule. References in his autobiography to the "fourth dimension," a realm of will power, and his practiced, hypnotic stare reminded many Poles of a Russian "mind-control showman" who appears on Polish television.

This week, the Polish press published photographs of a bare-chested Tyminski draped with boa constrictors in Peru. The candidate angrily denied published allegations by former associates in Canada that he had abused his wife and deprived his children of food.

On Friday, Tyminski's final campaign rally was nearly drowned out by pro-Walesa hecklers, some of whom wore costumes of South American Indians. Others shouted, "Do svidanya" -- Russian for "goodbye," a reference to unsubstantiated but widely reported charges that Tyminski had functioned as an agent of the KGB, the Soviet security police.