Vice President Biden was in Warsaw last week to reassure our eastern NATO allies that they have the support of a “steadfast ally.” But if Russia moved against Poland or the Baltic States, would the United States really go to war? Or would we do nothing and effectively destroy the NATO alliance?

President Obama has ruled out a “military excursion” in Ukraine. America is not obligated legally to take action against Russia for annexing Crimea. We would not go to war if Russia mounted a large-scale invasion of Ukraine to restore the ousted, pro-Moscow government of Viktor Yanukovych, currently under U.S. sanctions. And we would not even send troops if Ukraine was partitioned, or absorbed by Russia. Americans have no interest in such a conflict, and no stomach for it.

NATO allies are a different matter. The North Atlantic Treaty is a mutual-defense pact, and Article 5 says that an armed attack against one member state “shall be considered an attack against them all.” This is a clear red line. The only time Article 5 has been invoked was in the wake of the September 11, 2001 terrorist attacks, and most NATO allies sent troops to support the efforts in Afghanistan and Iraq.

Could the current crisis expand to touch NATO? The developing situation in Ukraine has been compared to Germany’s absorption of Austria in 1938, or the subsequent partition and dismemberment of Czechoslovakia. Hillary Clinton compared Russian president Vladimir Putin to Adolf Hitler, which by extension puts President Obama in the role of British prime minister Neville Chamberlain, who famously failed to achieve “peace in our time” at Munich.

Push the analogy further. The Second World War was sparked by Warsaw’s resistance to Berlin’s demand to annex the Polish Corridor, a small stretch of land—smaller than Crimea—separating the German provinces of Pomerania and East Prussia. Hitler responded by invading Poland and partitioning it with the Soviet Union. Britain and France had pledged to defend Polish independence, and two days after Germany invaded, they declared war. In his war message, Chamberlain explained that Hitler’s actions showed “there is no chance of expecting that this man will ever give up his practice of using force to gain his will. He can only be stopped by force.”

This may or may not describe Mr. Putin, as Mrs. Clinton alleged. But if similar circumstances arise in the near future, will the United States honor security guarantees made to Poland and the Baltic States when the Russian threat was only a theory?

Mr. Biden stood with Estonian president Toomas Ilves Tuesday to “reconfirm and reaffirm our shared commitment to collective self-defense, to Article 5.” He wanted to make it “absolutely clear what it means to the Estonian people” and that “President Obama and I view Article 5 of the NATO Treaty as an absolutely solemn commitment which we will honor—we will honor.” Shortly thereafter, Moscow “expressed concern” about the treatment of ethnic Russians in Estonia. Mr. Putin justified his actions in Crimea as “restoring unity” to Russian people. Estonia’s population is 25 percent ethnic Russian, compared to 17 percent in Ukraine, mostly in the north and east part of the country. Suppose anti-Russian riots “spontaneously” broke out in Estonia. What would the United States do if Moscow invoked a “responsibility to protect” these people and bring them “back” to the Motherland? Would President Obama take military action against Russia over a small, secluded piece of a tiny, distant country? Would it be like the Polish Corridor in 1939? This is highly doubtful—highly doubtful.

Aren’t we obligated by treaty to intervene? Mr. Biden mentioned the “absolutely solemn commitment which we will honor.” It was so important he said it twice. However, Article 5 says that NATO members pledge to come to the assistance of the attacked state using “such action as it deems necessary, including the use of armed force.” It doesn’t take a White House lawyer to see the gaping loophole—President Obama can simply deem that the use of U.S. force isn’t necessary. He can walk back the red line, as he did with Syria. Stern talk and minimal sanctions would follow, but Estonia would lose some, if not all of its territory. And in practical terms it would mean the end of NATO, which is one of Moscow’s longstanding strategic objectives. Mr. Putin’s chess game does not end in Crimea.

James S. Robbins is Senior Fellow in National Security Affairs at the American Foreign Policy Council in Washington, DC.