Hundreds of thousands of Ukrainians filled the streets of Kiev on Sunday — no longer focused solely on a trade agreement with the European Union, but also turning their attention to recasting their country’s frayed and corrupt political system.

The demonstrators represent disparate strains within Ukraine and do not have a cohesive leadership to guide them. They face steep odds in their effort to force embattled President Viktor Yanukovych to resist the heavy pressure that Russia is exerting to keep Ukraine in its orbit.

Yet the sheer numbers demanding closer ties with Europe and a government that listens to its people has pushed the rickety Ukrainian political system closer to the breaking point.

Despite threats of serious criminal charges, columns of marchers expanded their hold on the center of the capital, establishing satellite camps outside Kiev’s main square and toppling a statue of Soviet state founder Vladimir Lenin. They burned firewood in barrels to ward off the cold.

Opposition leaders called on demonstrators to surround all government buildings, at least until Yanukovych fires Prime Minister Mykola Azarov and his cabinet, and new elections are called.

The Post's Moscow Bureau Chief, Kathy Lally, explains why Ukrainians are protesting in the streets. (Sandi Moynihan/Kathy Lally, Sandi Moynihan and Terri Rupar)

But the government announced that the mostly young occupiers have until Monday to vacate City Hall, where they have set up a headquarters and where it appears a showdown may occur.

More than two weeks of demonstrations on the cold streets of Ukraine’s capital — the largest since the country’s Orange Revolution in 2004 — have hardened and inspired the protesters. At first, they simply wanted Yanukovych to sign a trade pact with the E.U., as he had been promising. Now, they want a new Ukraine — free of corruption, ruled by law, and with honest elections and politicians.

But the various groups in the streets have different political convictions, ranging from liberal to far right. Little unites them beyond a distaste for Yanukovych’s government. Their leadership is fragmented, and they lack a pragmatic and achievable agenda.

[READ: Major players in the protests]

“Everyone wants the president to go away, but they know it’s unrealistic,” said Anton Symkovych, professor of sociology at the National University of Kiev-Mohyla Academy. “They need goals, but combating corruption or moving toward Europe aren’t clear goals. There are no leaders.”

President under pressure

The protesters are young and old, urban and rural. The young — the generation that grew up after the fall of the Soviet Union — make up the largest single group.

“We’ve always seen Ukraine as independent, and not as a small Russia,” said Anastasia Bondarenko, 23, who has been demonstrating every day since Nov. 21. “The protests are transforming people. They’re starting to care about problems beyond themselves. They are beginning to self-
organize. That is a big change.”

When the crowd toppled and beheaded the Lenin statue at one end of Kiev’s main avenue, near the venerable Bessarabsky market, police watched but did not intervene. After singing the national anthem, protesters shouted, “Yanukovych, you’re next!” An extremist nationalist organization asserted responsibility for the incident.

This is Yanukovych’s second revolution. The country rose up against him in the Orange Revolution, reversing his victory in a fraudulent election, but he made a comeback and was voted into the presidency in 2010.

European Commission President José Manuel Barroso urged Yanukovych in a telephone conversation Sunday to talk with the opposition and civic groups to find a peaceful solution to the protests.

Yanukovych, a native Russian speaker from the eastern part of the country who had to learn the Ukrainian language when he entered national politics, has personal reasons for wanting to keep his job. His family has become wealthy during his time in office — Ukrainian journalists report that Yanukovych’s dentist son is one of the country’s richest men.

Also, Yanukovych limited political competition by jailing his opponents. He would expect them to do the same to him if he lost power.

A heavyweight neighbor

Just to the east of this nation of 46 million, Russia casts a threatening shadow.

President Vladimir Putin has made it a priority to persuade Ukraine to turn away from Europe and enter into a Russian-organized Customs Union. Ukraine is on the verge of bankruptcy, and its gas debt to Moscow — amounting to more than $2 billion — gives Putin enormous leverage.

Rumors that Yanukovych promised to enter the union when he met with Putin on Friday exacerbated anger among the protesters, despite denials of any agreement by both countries.

[A reader’s guide to the protests in Ukraine]

The majority of Ukrainians trust none of their political leaders, neither those in the president’s party nor those in the opposition, according to a poll conducted just before the demonstrations began. In the survey, 87 percent expressed unhappiness with the economy and 79 percent with the political situation. The poll was sponsored by the U.S. Agency for International Development.

“During the Orange Revolution,” Bondarenko said, “people did believe in leaders. Now they don’t.”

Protester Anatoliy Khomenko, a 23-year-old account executive with a public relations firm in Kiev, said he doubted that new, trusted leaders will emerge before presidential elections in 2015. And if the protesters lose, and the government clamps down on them as Russia did on its opposition, there will be no new leaders.

“This has been a protest originating from common citizens rather than politicians,” Khomenko said. “What we see now is the government trying to outlast the protesters.”

Looking toward Europe

Some Ukrainians argue that the protesters are placing misplaced hopes on the European Union and the “association agreement” that Yanukovych refused to sign.

“It’s 2,000-and-some pages that has never been translated into Ukrainian,” said Roman Kultinsky, a 36-year-old translator. “No one has ever read it. The main emphasis is on European values. That’s a very broad term.”

The E.U. doesn’t intend to make Ukraine a full member of the bloc, Kultinsky said, because it has enough problems with the debt-ridden countries that are already part of it. He said the broad umbrella nature of the protests is inherently risky because the nationalist extremists have joined in.

“These guys have a precise ideology,” Kultinsky said, “and although they are in the minority, they are better organized. That’s a real danger.”

Symkovych, the sociology professor, said small victories have already been won. In his home town of Uzhhorod, in western Ukraine, students attended a meeting of the city council, whose members were accustomed to making all their decisions in secret. But after the students confronted them, the council members voted to make all of their deliberations public.

The other day, Symkovych visited the Kiev City Hall, where protesters have occupied two floors. It was amazingly clean and well run, he said.

“I was impressed,” he said. “It’s the first time we’ve had genuine self-government.”

Those out on the streets don’t know what comes next. The protest was so unexpected, they say, that the next step is hardly predictable.

Bondarenko said she and her friends have no illusions that signing the association agreement with the E.U. will turn Ukraine into a different country overnight.

“We understand Europe has lots of problems,” she said. “But they have a set of rules. They know how to follow the rules. We want to follow rules.”