But that reality apparently has not sunk in. If anything, Mr. Putin has grown more belligerent, focusing new fire on Mariupol as Russian forces seek to secure all of the Donbas region in the coming weeks. He has insisted to visitors like Mr. Nehammer that he remains determined to achieve his goals.

While Russian casualties have been high and Mr. Putin’s ambitions have narrowed in Ukraine, American intelligence assessments have concluded that the Russian president believes that the West’s efforts to punish him and contain Russia’s power will crack over time. With the help of China, India and other nations in Asia, he appears to believe he can avoid true isolation, just as he did after the annexation of Crimea in 2014.

Now, American officials are girding for what increasingly feels like a long, grinding confrontation, and they have encountered repeated reminders by Mr. Putin that the world is messing with a nuclear weapons power and should tread carefully.

On Wednesday, after providing warnings to the Pentagon that a missile test was coming — a requirement of the New START treaty, which has four years remaining — Mr. Putin declared that the launch should “provide food for thought for those who, in the heat of frenzied aggressive rhetoric, try to threaten our country.”

In fact, the missile, if deployed, would add only marginally to Russia’s capabilities. But the launch was about timing and symbolism: It came amid the recent public warnings, including by Mr. Burns, that there was a small but growing chance that Mr. Putin might turn to chemical weapons attacks, or even a demonstration nuclear detonation.

If Mr. Putin turns his sights on the United States or its allies, the assumption has always been that Russia would make use of its cyberarsenal to retaliate for the effects of sanctions on the Russian economy. But eight weeks into the conflict, there have been no significant cyberattacks beyond the usual background noise of daily Russian cyberactivity in American networks, including ransomware attacks.