The political crisis in Ukraine has reached a critical turning point, at which each side must consider what it stands to lose from further conflict. On Saturday, President Viktor Yanukovych unexpectedly offered serious concessions to opponents camped out on the Maidan, as Independence Square in Kiev is known, including senior government posts to two of the opposition leaders. On Tuesday, his prime minister and close political ally, Mykola Azarov, resigned, while the Parliament voted to repeal most of the laws passed earlier in the crisis limiting freedom of speech and assembly. Then on Thursday, the president went on sick leave, but without signing into law the repeal, leaving both the measure and a broader, negotiated solution with the opposition hanging in the air.

Mr. Yanukovych has to be aware that his grip on power is slipping fast, and that his political survival depends on cutting a deal. That might seem to argue for the opposition to continue fighting until his corrupt administration is ousted. But danger lies that way. For one thing, the Ukrainian economy is disintegrating. The Russian aid that helped persuade Mr. Yanukovych to reject an agreement with the European Union last November — and thus triggering the protests — has provided a slim financial lifeline. Perhaps ominously for Mr. Yanukovych, reports from Kiev on Wednesday suggested that Russia might refuse to come through with the next $2 billion of its $15 billion package.

Another problem is that the opposition is united largely in its disgust with the corruption and authoritarianism of the Yanukovych-led political elite and a vague longing for Westernization and transparency. Beyond that, the protesters are sharply divided. The differences were on display Wednesday when five people were wounded in a spat over who would control the occupied building of the Agriculture Ministry.

No matter how incompetent, discredited or unhealthy he may be, Mr. Yanukovych is the democratically elected president, and to oust him by street protests and without a coherent plan or united leadership would be a recipe for further turmoil and a dangerous precedent.