Let us stipulate that Ukrainian President Viktor Yanukovich has blood on his hands for the massacre of protesters in Kiev, and that Russia’s President Vladimir Putin—who seems to view the repression of Ukraine’s opposition with equanimity—bears a lot of guilt for the killings. And let us hope that the cease-fire reached overnight in Kiev, after much to-ing and fro-ing by Western diplomats and desperate phone calls from Vice President Joe Biden, will hold—though it isn’t likely.

Now what? Well, though the United States has little leverage, Washington could start by letting Moscow know that it doesn’t want Ukraine to blow up.

To American hawks and neoconservatives, the crisis in Ukraine ought to trigger a muscular American response. A Wall Street Journal editorial blames “Western passivity” for Ukraine’s tumble into near–civil war conditions, blaming the Obama administration for not taking stronger measures, such as freezing Ukraine’s financial assets. Writing in The Wall Street Journal, Peggy Noonan says:

It is particularly important now for us to show the people of Ukraine, and of Europe, that America is not some exhausted shell of itself with no adherence to anything larger than the daily concerns of its welfare state, but still a nation with meaning.

And hawks in Congress are demanding, among other things, that the United States immediately offer membership in NATO to Georgia, apparently seeking deliberately to widen the crisis and further provoke Russia. Additionally—and again in the Journal—Bernard-Henri Lévy, the reliable old war horse, demands that the United States pull out of the Sochi Olympics, which would accomplish precisely nothing.

And there’s more. Anna Borschchevskaya, writing in National Review, says: “This is one battle the U.S. cannot ignore.” And Ariel Cohen, the venerable neoconservative at the Heritage Foundation, writes: “An East-West confrontation may be imminent.” But Cohen has little to offer as to steps that the United States might take other than sanctions and, well, bluster.

The tough talk from hawks is expected. But what’s evident in reading their prescriptions is that there is really little or nothing that the United States can do, except perhaps what it’s already doing, namely, having talks with the government of Ukraine and the opposition (at least the mainstream representatives of the opposition), and trying to bring Western Europe and even Moscow into the picture—though contacts with Moscow, at least directly, seem few and far between.

You don’t have to look far for evidence of the lack of American leverage in Ukraine. Take, for example, the inability of the Secretary of Defense Chuck Hagel, the Pentagon and US military leadership even to get Ukrainian leaders to answer the phone.

As USA Today reports:

Hagel spoke with [Ukrainian Minister of Defense] Lebedev on Dec. 13 and ‘warned Minister Lebedev not to use the armed forces of Ukraine against the civilian population in any fashion,’ according to a statement issued then by Pentagon spokesman Carl Woog…. Other Pentagon leaders, including Gen. Philip Breedlove, the head of the U.S. European Command, have attempted to reach the Ukrainian military without success, said Col. Ed Thomas, a spokesman for the Joint Chiefs of Staff.

Hagel has since attempted to call the Ukrainian Ministry of Defense as the situation worsened, but “the Ukrainian defense minister won’t take Secretary of Defense Chuck Hagel’s calls; in fact, no one at the defense ministry will even answer the phone,” according to Stars and Stripes.

USA Today headlined its article: “Hagel not able to engage Ukrainian counterpart.” And Stars and Stripes says Rear Adm. John Kirby “described the situation as ‘pretty unusual,’ and said nothing like this has ever happened to Hagel since he took office.”

The very nature of the shocking police assault on the protesters may itself be Yanukovich’s undoing, since he’s now losing control both of his own party and of Ukraine’s fractious parliament, plus apparently losing the backing of some of the oligarchs who’ve supported him until now. If so, it’s possible that the accord will lead to new presidential elections, almost certain to empower the pro-Western (and anti-Russian) political powers in Ukraine.

How that will sit with Putin isn’t clear. Putin has both defensive reasons—opposition to the expansion of the European Union and NATO to Russia’s very borders to the south and west, and vast economic interests in Ukraine that he hopes to integrate into a revived Russian power—and offensive reasons for pressing Russian influence in Kiev. The editor of Russia in Global Affairs—on whose board sits Sergey Lavrov, the Russian foreign minister, along with other prominent Russians, including a former ambassador to the United States is Fyodor Lukyanov. Writing for the BBC, Lukyanov describes Putin’s view thus:

In his view, unrest must be suppressed before it turns into a huge fire. Unrest produces nothing but chaos. A weak state drives itself into a trap. Once a state falters, external forces will charge through the breach and start shattering it until it falls. The West is destructive. It is either unable to understand the complexity of the situation and acts in a primitive way, designating “good” and “bad” players, or it deliberately destroys undesirable systems. The result is always the same—things get worse. The desire to limit Russian influence and hinder Moscow’s initiatives is the invariable imperative of the Western policy.

And he adds:

Putin fears chaos. The main driving force behind his policy towards Ukraine will be not a desire for expansion, but a desire to reduce the risk of chaos spilling into Russia. To this end, anything goes—both defensive and offensive means.

It ought to be the role of the United States to ease tensions in Ukraine, by backing off, supporting a smoother European-Russian dialogue (one in which the words “Fuck the EU” aren’t heard), and hoping for a commitment from all sides in the Ukrainian dispute to come up with a political solution that works. That may mean that Ukraine does indeed reorient toward a closer economic affiliation with the EU, or that it joins the confederation being assembled by Russia, or something in between. But, despite what’s being said by so many in the US establishment, Ukraine is hardly a top American national security interest.

Above all, easing tensions means letting Putin know that Washington isn’t seeking “chaos” in Kiev. And meaning it.