Despairing of finding enough beds for patients stricken with the coronavirus, a nurse in the Siberian city of Irkutsk has been forced to begin taking people to a village hospital more than 100 miles away.

And the worst is yet to come, said the nurse, Valentina M. Monkhoroeva, adding, “the number of confirmed cases in the Irkutsk region grows every day.”

As Monkhoroeva’s predicament illustrates, the pandemic is now advancing, not receding, across much of Russia’s vast hinterland. But that has not dimmed the Kremlin’s determination to hold a nationwide vote on constitutional amendments that, among other things, would enable President Vladimir Putin to stay in power until 2036.

With Moscow, some 2,600 miles to the west of Irkutsk, seemingly over the worst of the outbreak, Putin has declared victory over the coronavirus and mobilized huge resources to make sure the referendum, already put off once, now goes ahead no matter what. Voting officially started last Thursday but the big day is Wednesday, which has been declared a national holiday in the hope that more people will vote.

Across much of Russia, the Kremlin’s zeal to press on with its plans regardless has encountered little or no resistance: Most people get their news from state television, while local legislatures are mostly controlled by obedient loyalists from Putin’s governing party, United Russia.

In Irkutsk, however, Putin’s party is in a minority, and his desire to put his own political future ahead of public health has fueled an unusual outbreak of alarm and public criticism.

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The regional Parliament, whose members include a large group of noisy Communists, has been forthright in its skepticism about the wisdom of declaring the coronavirus crisis over and about whether the situation is safe enough to hold a vote.

At a combative June 16 meeting, deputies grilled local officials in charge of the coronavirus response over why a decision had been taken before the referendum to lift restrictions that had been imposed to protect public health.

Olga N. Nosenko, a Communist member of the Irkutsk assembly and its deputy speaker, said she didn’t believe it was safe for her to go out to vote.

“I don’t understand why this voting is needed at all,” Nosenko said in a telephone interview. “All decisions have already been made.”

Indeed, the outcome of the yes-or-no vote on constitutional amendments — almost certain to be a resounding “yes” — will do nothing but confirm changes already enacted into law months ago by the national Parliament in Moscow.

All the same, the ballot has been invested with huge significance by the Kremlin, which sees it as a way to confer popular legitimacy on a contrived maneuver intended to give Putin, already in power for 20 years, the option of staying in office for another 16 years.

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With his approval ratings at their lowest level since he came to power at the end of 1999, the decision to hold the national vote despite coronavirus concerns suggests that Putin wants to rush the process before the economy, already badly damaged by the pandemic, deteriorates further and his ratings run the risk of slumping even more.

On Sunday evening, state television featured a gushing special report describing how Russia, in contrast to the United States, had subdued the coronavirus and detailing all the precautions that had been taken, including single-use disposable pens and free gloves, to ensure that polling stations were safe.

“Without any doubt, we were generally able to complete the task that we set ourselves — to protect Russian citizens from this infection,” Putin said in a television interview broadcast on June 21.

The number of new infections is indeed falling in Russia, but that is the result mostly of a steep decline in new infections in Moscow, the initial epicenter of the pandemic in the country.

The situation in Irkutsk and other far-flung places looks very different.

As a general rule, the more distant the region is from the capital, the later it has been hit by the virus. Over the past week, the pandemic entered its worst stage so far in a diverse set of Russian regions, including the Republic of Tyva on the border with Mongolia, which is now the worst-affected region in Russia in terms of infections per capita. Also badly hit is the Republic of Karachay-Cherkessia, an isolated area in the North Caucasus.

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While the daily number of new cases in Moscow has been falling since May, Irkutsk and the surrounding region have seen a steady acceleration in the outbreak over the same period. Local health officials warn that the pandemic reached its peak only in the middle of June.

Despite this, local authorities have largely followed the lead of Moscow, which went into strict lockdown at the end of March but has now lifted most restrictions.

“I don’t see any logic in the way these decisions were made,” said Zoya V. Kuznetsova, an editor of Ircity.ru, a local news outlet in Irkutsk.

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There is the same disconnect in the neighboring Zabaikalsky region. Andrei V. Kozlov, an editor of Chita.ru, a regional news website, said that local residents had watched national television and seen Putin announce that the battle was basically won just as “the number of new cases in Zabaikalsky was at its peak.”

Regional officials say they have things under control. In a written response to questions, Natalia P. Ledyaeva, the Irkutsk region’s health minister, said that there was no shortage of hospital beds in the region as a whole, with only 58% of available beds currently taken. The city of Irkutsk did not immediately respond to a request for comment.

From the start of the pandemic, Putin has repeatedly said that Russia’s vast territory means it would be foolish to have a “one-size-fits-all” approach. So he left it up to regional leaders to decide whether they wanted to follow Moscow’s lead and hold parades on June 24 to celebrate the 75th anniversary of Nazi Germany’s defeat.

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Many declined, including the governor of Irkutsk, Igor I. Kobzev, who said that holding a parade would be too risky.

Opting out of voting on the constitutional changes, however, is not an option. The only leeway that regional leaders have been given is on what measures they take to ensure that voters turn out. As a result, officials across the country have been busy dreaming up imaginative ways — among them raffles, grocery vouchers, clown shows, free cakes and other incentives — to get out the vote.

On Friday, a day after voting starting, the Irkutsk governor ordered that a “regime of self-isolation” be extended until July 12 and banned all “mass events.” Voting, however, is exempt from the restrictions.

But with nerves on edges because of the pandemic and mounting economic hardship, not everybody is going along with the program.

Particularly vocal in Irkutsk have been the Communists.

The party issued a statement denouncing the referendum as “meaningless and illegitimate” and as a “parody” that would “condemn the country to lawlessness and inhuman capitalism.”

Aleksei V. Petrov, a local historian, said that the Communist Party was “the most powerful political force,” not necessarily because voters shared its ideology but because it was well organized, had deep roots and sometimes dared to go against the Kremlin-imposed grain.

The party’s opposition certainly will not derail the referendum, but combined with growing alarm about the coronavirus in areas only now being pummeled and a widening economic crisis across much of the country, it does point to bubbling dissatisfaction beneath Russia’s placid political calm.

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Monkhoroeva, the Irkutsk nurse, said in an interview on Saturday, two days after voting started, that there was still a shortage of ambulances in Irkutsk.

“The peak is not over,” she said.