Russian troops are encircling Ukraine from three sides. In Washington and Brussels, there are warnings of crushing sanctions if Vladimir V. Putin orders an invasion. Embassy families — both American and Russian — are being evacuated from Kyiv.

Yet there are still diplomatic options — “offramps” in the lingo of the negotiators — and in the next several days the Biden administration and NATO are expected to respond, in writing, to Mr. Putin’s far-reaching demands.

The question is whether there is real potential for compromise in three distinct areas: Russia’s demand for ironclad assurances that Ukraine won’t enter NATO; that NATO won’t further expand; and that Russia can somehow restore some approximation of its sphere of influence in the region to before the strategic map of Europe was redrawn in the mid-1990s.

The hardest issue of all defies negotiation: Mr. Putin’s demand that Ukraine reverse its “drift” toward the West. That is a matter of national sentiment, and polls show that in the years since Russia’s seizure of Crimea in 2014, Ukrainians are more desirous than ever of joining the Western alliance. Mr. Putin’s massing of the troops is likely to accelerate that trend, American officials say, rather than reverse it.And as in all conflicts with roots in the Cold War and its aftermath, the subtext of any negotiation includes how the world’s two largest nuclear-armed states manage their arsenals — and use them for leverage.

While there is still time to avoid the worst, even President Biden’s top aides say they have no idea if a diplomatic solution, rather than the conquest of Ukraine, is what Mr. Putin has in mind. The Russian president views Ukraine not as a separate nation but as a land that was negotiated away after the collapse of the Soviet Union. Many who have dealt with Mr. Putin believe he now sees it as his mission to correct that error, even if that means risking war to redraw the map of Europe.

Even if the diplomacy is for real, no one is certain how long they have to head off military action. A few weeks? Until the end of the Beijing Winter Olympics, on the theory that Mr. Putin would not want to anger President Xi Jinping by starting a war that would divert attention from China’s big moment?

Not all the potential blockades to a solution involve the Russians. If facing down Moscow was once a bipartisan task in Washington, it is no longer. Even before the counterproposals to Russia are finished, Republicans have been using the tensions to portray the administration as offering “appeasement,” a word chosen to evoke images of Britain’s approach to Nazi Germany in the 1930s.

Secretary of State Antony J. Blinken, trying to blunt the angle of attack, shot back on Sunday that “engaging in diplomacy doesn’t take the word ‘nyet’ out of your vocabulary.”

It is possible that Mr. Putin’s bottom line in this conflict is straightforward: that he wants to stop Ukraine from joining NATO and get an assurance that the United States and NATO will never place offensive weapons that threaten Russia’s security in Ukrainian territory.

On those two issues, it would seem, there is trading space. While the United States says it will never abandon the NATO “open door” policy — which means that every nation is free to make its own choice about whether it seeks to join the Western alliance — the reality is clear: Ukraine is so corrupt, and its grasp of democracy is so tenuous, that no one expects it to be accepted for NATO membership in the next decade or two.

On this, Mr. Biden has been clear.

“The likelihood that Ukraine is going to join NATO in the near term is not very likely,” he said at a news conference on Wednesday, giving voice to a previously unspoken truth. “So there is room to work if he wants to do that.”

It seemed an open invitation to offer Russia some kind of assurance that, for a decade, or maybe a quarter-century, NATO membership for Kyiv was off the table. But the Biden administration has drawn a red line at allowing Mr. Putin a right to veto which nations can join NATO.

More complex is negotiating the reverse problem: How the United States and NATO operate in Ukraine. Ever since the annexation of Crimea in 2014, the United States and NATO nations have been haltingly providing Ukraine with what the West calls defensive arms, including the capability to take out Russian tanks and aircraft. That flow has sped up in recent weeks.

To hear Mr. Putin, those weapons are more offensive than defensive — and Russian disinformation campaigns have suggested that Washington’s real goal is to put nuclear weapons in Ukraine. Administration officials say the United States has no such plans — and some kind of agreement should be, as one official said, “the easiest part of this,” as long as Russia is willing to pull back its intermediate-range weapons as well.

Mr. Putin has made clear that he wants to restore what he calls Russia’s “sphere of influence” in the region — essentially a return to the Cold War order, before Bill Clinton and Boris Yeltsin agreed in 1997 that former Soviet states and Warsaw bloc nations could choose whether to seek membership in NATO. Since then, the alliance has roughly doubled in size.