Following long days of street warfare, which led to the first deaths since antigovernment protests began in November after Ukrainian President Viktor Yanukovych refused to sign an association agreement with the European Union, Yanukovych signaled this week that he might be ready to acknowledge some of the opposition’s demands. On Monday, he announced that the anti-protest laws his government had passed on November 16 would be scrapped. Then, on Tuesday, Prime Minister Mykola Azarov resigned. At first blush, this might have seemed like a perfect opportunity for Ukraine’s three opposition leaders -- Vitali Klitschko, Oleh Tyahnybok, and Arseniy Yatsenyuk -- to step in and take his place. Instead, it put them in a difficult situation and highlighted the tensions between them and the protesters.

That might have been precisely what Yanukovych intended the Saturday before, when he offered Azarov’s job to the opposition. He tapped Yatsenyuk, who leads the imprisoned Yulia Tymoshenko’s Fatherland party, as the potential prime minister, and Klitschko, the world-boxing champion and leader of UDAR (the Ukrainian Democratic Alliance for Reform, literally “punch”), as deputy prime minister for humanitarian affairs. The announcement was not greeted with much enthusiasm on Kiev’s Independence Square, known as the Maidan. When the opposition leaders, emerging from three hours of talks with Yanukovych, appeared to reject the offer, it prompted a sigh of relief. “No deal @ua_yanukovych, we're finishing what we started,” Yatsenyuk tweeted in English later that evening. “The people decide our leaders, not you.”

For all that bravado, however, Yatsenyuk and Klitschko are in a difficult position. Rejecting Yanukovych’s deal would make them appear unwilling to negotiate. After all, for some Ukrainians, the offer might seem like a welcome chance to lower tensions following the worst week of clashes since the protests began. But accepting the deal would brand Yatsenyuk and Klitschko as traitors in the eyes of the protesters, many of whom have been out in the cold for weeks. It would also hurt their chances of beating Yanukovych in a presidential election next year.

The protesters’ relief highlights their lack of trust in the opposition leaders, whom they feared might take Yanukovych’s bargain and then be co-opted by him. They are not on the Maidan because they are pro-Klitschko or pro-Yatsenyuk but because they are anti-Yanukovych and want early elections. It is true that Azarov will not be missed on the Maidan, where he is the target of numerous jokes and has further angered people with his claims that the authorities had nothing to do with the deaths last week. But the protesters’ wrath is focused on Yanukovych, and it is possible that many will not go home until he leaves.

Yanukovych’s offer might also have stirred up rivalries among the three opposition leaders, who banded together following the 2012 parliamentary elections. Even before the deal, they were divided over who would run in 2015 -- one opposition candidate or all three. Klitschko, who early polls suggest has the best chance of beating Yanukovych in a presidential standoff, was proffered only the modest post of deputy prime minister for humanitarian affairs. The more senior position was offered up to the more experienced but less popular Yatsenyuk.

Meanwhile, Tyahnybok, the leader of the nationalist Svoboda (“Freedom”) party, was left out. Rather than enabling Klitschko and Yatsenyuk to distance themselves from the far-right leader, the deal would have allowed Tyahnybok to proclaim himself as the only opposition leader still loyal to the protesters. Extreme right-wing views are restricted to a minority of protesters. Yet the departure of moderate politicians such as Klitschko and Yatsenyuk could make it easier for Tyahnybok and even more radical forces, such as Pravyy Sektor ("Right Sector"), a loose alliance of nationalist organizations that gained prominence during the clashes last week, to try to dominate the protests.

On top of these risks, accepting Yanukovych’s offer would not give the opposition much room for action anyway, since Ukraine’s current constitution gives the prime minister only limited power. Over the weekend, Yanukovych said that he would be willing to return to the 2004 Ukrainian constitution, which was repealed in 2010. That was one of the opposition’s demands, as it would empower the prime minister at the expense of the president. (Tyahnybok says that his party, Svoboda, opposes this move.) Yatsenyuk has noted his preference for the formation of a constitutional committee that would consider revisions to the current power structure.

Yanukovych’s moves are first steps, but they hardly represent major concessions. The parliament’s decision this week to repeal the anti-protest laws is good news but, as many observers have pointed out, simply returns Ukraine to the status quo ante. And late on Wednesday, the parliament passed a law granting amnesty to people detained during the protests on the condition that protesters withdraw from the government buildings that they have been occupying. Angered by this condition, the opposition parties abstained from voting.

The appointment of Serhiy Arbuzov, the deputy prime minister and a loyal Yanukovych ally, as interim prime minister is no concession either. Discussions about who will replace Azarov are continuing. Even if the opposition stays out of government, Yanukovych may settle on a compromise candidate. Yet despite the first signs that protracted negotiations are leading somewhere, the situation remains fragile. Speaking in parliament on Wednesday, Leonid Kravchuk, Ukraine’s president from 1991 to 1994, warned that the country is “on the brink of civil war.” And that was not the first time those words have been uttered in the past few weeks.

“The most important [thing] today is to preserve the unity and integrity of Ukraine,” Azarov said in his resignation statement on Tuesday. “That is much more important than anybody’s personal plans and ambitions.” These words could yet come back to haunt Yanukovych as the opposition continues to demand early elections. Depending on how the situation develops, they may become increasingly relevant for the three opposition leaders too.