The liberal world order has been on life support for a while. President Biden, in his inaugural address, called democracy “fragile.” President Vladimir V. Putin of Russia said two years ago that “the liberal idea” had “outlived its purpose,” while China’s leader, Xi Jinping, has extolled the strength of an all-powerful state and, as he put it last March, “self-confidence in our system.”The multinational response to Russia’s invasion of Ukraine has shown that the demise of the global postwar rules-based order may not be inevitable. A month ago, no one predicted that Germany would reverse decades of military hesitancy and pour 100 billion euros into its defense budget, or that Switzerland would freeze the assets of Russian oligarchs, or that YouTube, World Cup soccer and global energy companies would all cut ties to Russia.But the reappearance of war in Europe is also an omen. With toddlers sheltering in subway tunnels, and nuclear power plants under threat, it is a global air raid siren — a warning that the American-led system of internationalism needs to get itself back into gear, for the war at hand and for the struggle against authoritarianism to come.“The global system was built in the 1950s, and if you think of it as a car from those years, it is battered, out of date in some ways, and could use a good tuneup,” said James Stavridis, a retired U.S. Navy admiral and former NATO commander in Europe. “But it is still on the road, rolling along, and, ironically enough, Vladimir Putin has done more in a week to energize it than anything I can remember.”Almost universally, from leaders in Europe and Asia to current and former American officials, Ukraine is being viewed as a test for the survival of a 75-year-old idea: that liberal democracy, American military might and free trade can create the conditions for peace and global prosperity.Because the founder of that concept, the United States, continues to struggle — with partisanship, Covid and failure in distant war zones — many foreign policy leaders already see Ukraine in dire terms, as marking an official end of the American era and the start of a more contested, multipolar moment.For at least a decade, liberal democracies have been disappearing. Their numbers peaked in 2012 with 42 countries, and now there are just 34, home to only 13 percent of the world population, according to V-Dem, a nonprofit that studies governments. In many of those, including the United States, “toxic polarization” is on the rise.For Ukraine and its democratically elected leaders, the prospects for survival look especially dim. Sanctions, the preferred weapon for the anti-Putin coalition, have a long history of failing to alter the behavior of rogue states or leaders. And for all the talk of defending freedom, Mr. Biden has repeatedly promised that no American soldiers will fight for Ukraine’s right to exist, even as a million refugees have already fled and Mr. Putin seems intent on taking the entire country.Ukraine may also be just the first of several tests for the old order. Mr. Xi, the Chinese leader, said a few months ago that “reunification” with Taiwan — another democracy living in the shadow of an authoritarian neighbor — “must be fulfilled.”Mr. Biden, in his State of the Union address on Tuesday, spoke bluntly of the future risk, saying, “When dictators do not pay a price for their aggression, they cause more chaos.” He insisted that the free world was holding Mr. Putin accountable.And even some skeptics do see signs of a liberal revival. Ryan C. Crocker, a retired former U.S. ambassador to Iraq and Afghanistan, said that after the disastrous American withdrawal from Kabul, the Biden administration had proved that the United States could still lead and gather together a strong global response.Robert Kagan, a conservative historian whose latest book, “The Jungle Grows Back: America and Our Imperiled World,” has been widely cited during the Ukraine conflict, said he too had been pleasantly surprised by how quickly the liberal order had “snapped back into place.”“There has been a significant reconfirmation of a lot of the old lessons we learned a long time ago and forgot about,” he said.One lesson seems to be that alliances matter. But for many, the most important lesson echoes what Franklin D. Roosevelt and Harry S. Truman concluded about World War II: America cannot retreat into isolationism; its own prosperity depends on actively trying to keep the world’s major powers at peace.Updated March 6, 2022, 7:55 a.m. ET“We have become increasingly indifferent — that’s why the Putin example has been so striking,” Mr. Kagan said. “A lot of people had a comforting and benign view of what a post-American world would look like — it would just be adjusting to other people having different opinions — so for the consequence to be war, it’s shocking to people.”“It should make them rethink their earlier assumptions about what America should be doing,” he added.Any attempt to rebuild a model of intervention, however, must deal with fraught recent history. The costly “war on terror” that followed the attacks of Sept. 11, 2001, shifted the country’s focus and undermined the world’s confidence in American intentions and competence.Invading Iraq despite global protests, seeing wars drag on for decades without much progress — it was all too much for the American public, Vanda Felbab-Brown, a senior fellow at the Brookings Institution, said in an interview from the Libya-Tunisia border.“You have this exhaustion of dying for nothing,” she said. “For the Taliban to come back to power, and with corrupt Iraqi politics run by Iran.”The American way of the world took another hit with the 2008 global financial crisis. Wall Street and Washington, not Moscow or Beijing, created economic havoc without addressing a surge of inequality tied to globalization. Then came President Donald J. Trump, who turned all the frustration into an inward-looking campaign of grievance.In his view, the United States had become a victim rather than a beneficiary of the “rules-based order.” European nations, for Mr. Trump, were not allies but hangers-on. And while Mr. Biden has since argued that “America is back,” most of the world is still asking: For how long?Polls have consistently shown declining interest in international affairs among Americans and declining faith in the ability of democracy to deliver. Political divisions have reached levels high enough for comparisons with the Civil War.“The biggest challenge to the system is the domestic basis of American power,” said Ivo Daalder, the president of the Chicago Council on Global Affairs and an ambassador to the North Atlantic Treaty Organization under President Barack Obama. “It’s still the only global military power, it’s still the largest economy and it’s the only power that brings other countries together. The question is: Does domestic politics allow America to play that leadership role?”After four years of “America First,” “there are,” Mr. Daalder said, “justifiable doubts.”Like Mr. Putin, Mr. Xi has more than just doubts.Ian Storey, a senior fellow at the ISEAS-Yusof Ishak Institute in Singapore, said that what’s happening in Ukraine “will not change Xi’s ideological beliefs one iota.”While the resistance to the invasion may inform his calculations on Taiwan, China’s most powerful leader in decades ultimately believes that “the U.S.-led Western world is fading and authoritarianism is the future,” Mr. Storey said. “While the liberal order has rallied to Ukraine’s defense, he will see this as a blip.”To be more than that, many argue, American politics needs to heal — fast. The country’s leaders have to explain the value of engagement, as Roosevelt did before World War II, historians note, and reinvigorate both American democracy and the institutions of the international order, which have yet to significantly change or expand their capacity to deal with the challenges of China and Russia.At the same time, other democracies must also take on more of the international burden, with money, defense and convening allies.Mr. Daalder envisions a system in which the world’s 12 or 13 largest democracies share leadership, “where the U.S. is maybe first among equals but still one among equals.”Michael Fullilove, the executive director of the Lowy Institute in Sydney and the author of a book about Roosevelt, described such a grouping as an ensemble in which countries like Germany and Australia step forward for larger roles.“The beneficiaries of the liberal international order have realized they must serve in its bodyguard,” he said.Mr. Crocker was one of many who laid out the stakes in the starkest of terms.“If we emerge from Ukraine with the narrative being that a united NATO, a united Europe, were able to face down Putin,” he said, then “we move forward to deal with the inevitable challenges ahead from a position of unity and American leadership.”If Russia takes over most or all of Ukraine and Mr. Putin is still in charge of a largely stable Russian economy, he added, “welcome to the new world of disorder.”