Originally Published: 26 MAY 22 11:14 ET

Updated: 26 MAY 22 12:30 ET

By Julia Horowitz, CNN Business

(CNN) -- When Ukrainian President Volodymyr Zelensky spoke by video to a packed room at the World Economic Forum in Davos, Switzerland, he thanked the West for its solidarity against Russia. But he also issued a warning to political leaders and business executives: Don't lose your nerve.

"I would only wish you not lose this feeling of unity," he said, calling again for maximum pressure on Moscow.

Three months after Russia's invasion of Ukraine, leaders from Europe and the United States emphasize that they remain committed to sticking with unprecedented sanctions in an attempt to force President Vladimir Putin to pull its troops out.

But as the cost of food and fuel jumps — fanning political protests and public discontent around the world, and increasing the risk of a recession — maintaining a consensus could prove increasingly challenging.

"I am very worried about what a recession in Europe would do to European resolve to stick with it and continue to escalate the sanctions," Jason Furman, a Harvard professor who previously served as President Barack Obama's top economic adviser, told CNN Business.

Already, cracks are starting to form in Europe's united front. Hungary's Viktor Orban, who was not present in Davos, has led dissenters in blocking the European Union's plans for an oil embargo on Russia, a bid to cut off a major source of revenue for Moscow. The goal of ultimately getting rid of Russian gas could prove even more difficult.

In the United States, President Joe Biden and Democrats are under enormous pressure to prove they're serious about fighting inflation ahead of the midterm elections in November, even though most factors causing it, such as supply chain snarls and high consumer demand, are largely beyond their control.

That could complicate efforts to continue to apply pressure on Russia, despite warnings from billionaire George Soros and others that appeasement of Putin would have catastrophic consequences.

Fuel and food prices shoot up

At Davos, leaders from government and business stressed that they cannot capitulate to Putin. They agreed that the response to his annexation of Crimea in 2014, as well as the poisoning of Sergei and Yulia Skripal in Salisbury, England in 2018, was far too weak in hindsight.

And the West's historic sanctions against Russia this year may not be enough, either. Russia's economy has been battered, but is holding up better than expected, bolstered in part by robust oil and gas revenues. That allowed the central bank to slash interest rates on Thursday.

"We have to stop compromising," Eduard Heger, the prime minister of Slovakia, said with emotion during a panel discussion. Compromising with Putin caused "an aggressive war," he continued.

Speaking to dinner guests, Soros warned that the invasion of Ukraine could mark the beginning of World War III, and said that Putin had to be defeated "as soon as possible" if the world wants to preserve civilization.

But the economic backdrop could make life harder for politicians back home. Annual Inflation among the 19 countries that use the euro reached 7.4% in April, an all-time high. In the United States, inflation stood at 8.3%, and it hit 9% in the United Kingdom.

A big factor is energy costs. They were already rising due to a supply and demand imbalance after the pandemic, but have been driven even higher by Europe's efforts to cut its dependence on Russian energy.

An oil embargo has been held up by landlocked states like Hungary and the Czech Republic, which say they would need years to make the transition to other suppliers or energy sources. It is expected to be agreed in the coming weeks, however.

"The economic situation is definitely challenging. I don't think it's going to impact consensus on oil," said Mujtaba Rahman, managing director for Europe at the Eurasia Group, a political risk consultancy.

Still, there will be consequences. Fears of energy shortages have already dramatically pushed up prices. In the United States, the average price of a gallon of regular gasoline reached a record $4.60 on Thursday. The situation is even worse in Europe. Recent data shows drivers in the United Kingdom paying $8.06 per gallon, and $8.43 per gallon in Germany.

At the same time, food prices are jumping as the war disrupts exports of key products such as wheat and sunflower oil, and as some countries like India subsequently enact export bans to protect domestic supplies. In April, food prices in Germany shot up 8.6% compared to the previous year.

"This is where the impact of the war in Ukraine is becoming more and more visible," Georg Thiel, president of Germany's Federal Statistical Office, said earlier this month.

European Commission President Ursula von der Leyen noted this week that "it is fragile countries and vulnerable populations that suffer most." She added that bread prices have increased 70% in Lebanon, and food shipments from Ukraine's Odessa haven't been able to reach Somalia, which is battling a devastating drought. Protests over rising prices have broken out in Peru and led to the prime minister's ouster in Sri Lanka.

However, even in Europe and the United States, lower-income households have increasingly been forced to choose between "heating and eating," which account for a bigger proportion of their budgets. Economists worry that a pullback in spending could trigger recessions, especially as central banks raise interest rates to try to tame inflation.

"There's real risk for lots of people," Oxfam International Executive Director Gabriela Bucher told CNN Business. Even in the "rich world," she added, there are people struggling "to fulfill their basic needs at the moment."

The British government acknowledged the problem Thursday when it announced a $6.3 billion windfall tax on oil companies to fund payments to people struggling with energy bills.

The future of Western solidarity

American and European officials and top corporate brass say Ukraine's victory is crucial. The brutal war and humanitarian crisis must come to an end, and democratic values have to prevail at what Germany's Scholz called a "turning point" for the world.

"It's hard to see any issue that has united people in the West as much as this issue," David Rubenstein, the billionaire founder of the Carlyle Group, told CNN Business. "I don't think that the incremental increases that might be attributed to this with respect to inflation are going to change anybody's views."

American officials also see standing up to Putin as imperative to curtailing the ambitions of Chinese President Xi Jinping, who they say is closely watching how the situation plays out.

"Deterrence is a key here," said US Congressman Michael McCaul, the top Republican on the House Foreign Affairs Committee. "As Xi looks at what's happening in Ukraine, [he's asking,] 'Is it worth it?' And we have to persuade him that it's not."

But balancing politics and economic concerns won't be simple. Scholz conceded that "politicians have an important task to attend to" as they juggle different parts of their mandate from the public.

This could become a larger issue in the event of a major escalation by Russia, Rahman said. That could trigger louder calls for a full ban on Russian natural gas, which accounted for 45% of Europe's supplies last year. Much travels by pipeline, which makes it more difficult to find alternatives.

That's not on the table right now, though Scholz said Germany is working "flat out" to end its reliance on Russian gas as soon as possible. But if it came under serious discussion, it would be a trickier sell than anything else the West has so far proposed.

Companies, while telegraphing strong support for Ukraine, are also worried about growing pressure on their businesses. Herbert Diess, the CEO of Volkswagen, told CNN Business that the full effects of rising raw material costs and inflation wouldn't be apparent for another six or 12 months, creating a "really tough" operating environment.

"We should achieve something with sanctions," he said. "So far, we're going basically from escalation to escalation and we have no choice. So I think sanctions, yes, but then how are we going to end this?"

Henry Kissinger, the former US Secretary of State, sparked a backlash earlier this week when he appeared to suggest that Ukraine should agree to give up much of the Donbas and Crimea to Putin.

"Negotiations need to begin in the next two months before it creates upheavals and tensions that will not be easily overcome," Kissinger said. "Ideally, the dividing line should be a return to the status quo ante."

Zelensky compared Kissinger's comments to appeasement of Nazi Germany in 1938.

"I do not want to hear the word 'appeasement' anymore," European Parliament President Roberta Metsola said Wednesday, to applause.

Still, a weakening economy and high inflation could weigh on politicians as they return home, sparking a warning from NATO Secretary General Jens Stoltenberg.

"Freedom is more important than free trade," Stoltenberg told the Davos crowd. "The protection of our values is more important than profit."