The “February Revolution” in Ukraine may be just getting underway, and the future of the country may be unsettled, to say the least, for years to come, but the Obama administration needs to approach the situation with great care. That’s because Russia, Ukraine’s powerful next-door neighbor, has vastly greater national interest in Kiev than does the United States. (Indeed, America’s national interest in Ukraine is almost nil, and aside from vague formulations about the need to support “democracy”—something that doesn’t enter into the US vocabulary when dealing with, say, Saudi Arabia—the United States really has nothing to gain or to lose in Ukraine.) For the United States, its priority has to be centered on establishing a decent working relationship with Russia and its president, Vladimir Putin.

On issues from terrorism to energy, and above all in dealing with Iran and Syria, the United States needs Russia. That means, among other things, no victory dances in the end zone by the White House. So far, President Obama, Secretary of State John Kerry, and other US officials have kept in constant contact with Putin, Foreign Minster Sergey Lavrov and other Russian leaders. But it won’t be easy going.

Apocalyptic scenarios about Ukraine are far-fetched. It’s very, very unlikely that Russia will intervene militarily in Ukraine, despite warnings to that effect from Susan Rice, President Obama’s national security adviser, other American politicians and pundits, including The Washington Post, which said in an editorial on Saturday: “It’s possible Mr. Putin will try to use force to impose his dominion over Ukraine once the Sochi Olympics end this weekend.” And it’s equally unlikely that Ukraine, which is deeply split between the pro-Russian east and parts of the south and its more European-oriented west, will break apart. By all accounts, even Viktor Yanukovich’s own Party of Regions—to the extent that it hasn’t fallen apart—has abandoned him, condemning his actions in the deaths of scores of Ukrainians in the final days of the revolution. Still, it’s worrying that the tumultuous Ukrainian parliament, which ordered Yanukovich’s arrest for murder, has also passed a resolution eliminating Russian as one of Ukraine’s languages. That’s not a promising start if there is to be bridge-building in the new Ukraine.

Probably the last thing that the European Union (EU) ought to want is to bring Ukraine into membership, and if that happens it will probably be many, many years from now. Having spent half a decade dealing with the struggling nations of Southern Europe that have been on the brink of default and bankruptcy, it’s hardly a good idea for the EU to absorb Ukraine, which is not only bankrupt but politically in utter turmoil. Perhaps that’s why the United States and the EU have invited Russia to contribute to an economic bailout of Ukraine, which is not only politically astute but economically the right thing to do. Indeed, according to The Wall Street Journal, Russia’s Finance Minister Anton Siluanov, who spoke with US Treasury Secretary Jacob Lew on Sunday, even suggested that the EU and the International Monetary Fund could play a positive role. Said Siluanov:

The fund has the experience of supporting countries in difficult situations…and they have a well-established set of tools to help in such cases. Naturally, the IMF experience could help.

But other Russian politicians have issued far darker comments on the crisis in Ukraine. Earlier, of course, Russia had offered a $15 billion bailout package to Ukraine, but that was suspended last week and it’s unclear how much, if anything, Russia might be willing to chip in to prevent Ukraine from spinning into chaos economically.

It’s important to note that the very moment that power tipped from the Yanukovich government to the opposition, the Interior Ministry, the police and especially the armed forces either withdrew or stayed neutral. According to The New York Times, the protesters and the opposition leaders were in close contact with security officials to prevent an escalation of the crisis. And the armed forces, whose chief wisely refused to take phone calls from Secretary of Defense Chuck Hagel in the week before the departure of Yanukovich, didn’t want any part of a defense of the ancien régime.

“Please be assured that the armed forces of Ukraine cannot and will not be involved in any political conflict,” said a statement from the military command. And Ukraine’s chief of staff, Yuriy Ilyin, added: “As an officer I see no other way than to serve the Ukrainian people honestly and assure that I have not and won’t give any criminal orders.”