With gas at $5 a gallon, how much do you care about Ukraine?

How much does Ukraine really matter?

Only weeks ago, the question would have seemed outlandish, when the United States and its European allies seemed poised to intensify efforts to help Kyiv beat back, or even defeat, Russian President Vladimir Putin’s scorched-earth invasion army.

Yet as the war takes a punishing toll on both sides – and the Western alliance faces major new strains and stresses – the issue is assuming key importance.

How the allies decide it will indicate the strength of their perseverance and of their commitment to the core principle behind their strong early response to the invasion: the imperative of defending a fellow democracy against unprovoked assault by an autocratic power bent on its destruction.

While Western governments remain determined to prevent an outright Russian victory, their arms deliveries in the coming weeks will reveal how ready they are to equip Ukraine for a counteroffensive. On the political front, the European Union is set to decide whether to fast-track Ukraine’s request for membership.

On both counts, the authorities in Kyiv are worried they will meet with half-measures or hesitation.

Behind those worries are doubts about the alliance’s longer-term commitment, all the more so in the wake of remarks last week by Mr. Putin signaling his determination to stay in the fight. The Russian leader compared his Ukraine invasion to Czar Peter the Great’s 21-year war against Sweden in the early 1700s, framing both wars as historic moves to “reclaim” rightfully “Slavic” lands.

And an array of intensifying pressures seems to be taxing the alliance’s unity and staying power. The most visible is the variety of opinions about whether the goal is a clear defeat of Mr. Putin or an outcome short of that.

The opinion that really matters – expressing itself through a “coalition of the willing” built around Russia’s Baltic neighbors – is Washington’s. But the United States is not exempt from distractions affecting its allies too.

The first is inherent in democratic societies: the shifting nature of the political agenda. Yes, Ukraine remains a major preoccupation for policymakers in allied capitals. And recent polling has suggested that across Europe, a majority supports NATO doing more to help Ukraine.

But, nearly four months after the Russian invasion, other stories have been nudging the war off the front pages. In France, for example, tightly contested parliamentary elections; in Britain, a new showdown with the EU over Brexit; in America, gun violence and the congressional hearings on last year’s mob assault on the Capitol.

And, across the alliance, the shared crisis that seems most likely to test its long-term resolve: soaring inflation.

It’s the steep rise in the price of energy – to power industries and businesses, or fill up cars at gas stations – that is most alarming consumers. In a number of European countries, that’s directly related to their deliberate effort to wean themselves off dependence on Russian energy imports.

The EU agreed 10 days ago to reduce imports of Russian oil by 90% by the end of this year, though Hungary and Slovakia won exemptions due to their heavy dependence on such energy imports. This has been a major concern for both Ukraine and Washington: EU oil purchases have been funding Mr. Putin’s invasion to the tune of several hundred million dollars a day.

But the deeper concern in Kyiv is that as economic problems continue to gnaw at Western consumers, they will shift their governments’ focus from the war, which would tilt the situation on the battlefield in favor of the very autocrat the allies have pledged to punish.

For while Mr. Putin’s forces have already been dealt setbacks that seem likely to degrade his conventional military power for years to come, the Ukrainians have seen their towns and cities reduced to rubble and are suffering huge losses of their own. In Ukraine’s case, the casualties aren’t just uniformed soldiers. They include large numbers of civilians helping fight off the Russian invasion.

That helps explain Ukraine’s pleas for heavy weaponry and other help to inflict an early defeat on the Russians – and its concerns about European allies’ staying power.

In Washington, President Joe Biden has been cleareyed from the start about the costs involved in sanctioning Russia, and explicitly forewarned Americans of the need to bear them. But even he has had to move inflation to the top of his policy agenda, especially with the approach of midterm elections.

As for Europe, Estonia’s unerringly pro-Ukraine prime minister, Kaja Kallas, has starkly framed the challenge for the weeks ahead. Acknowledging that it was getting harder to sustain allied unity amid rising energy prices, she cited her own experience, as a teenager, of “liberation” from Soviet occupation of the Baltic States.

“Gas might be expensive,” she said, “but freedom is priceless. People living in the free world do not really understand that.”