Senior White House officials designing the strategy to confront Russia have begun quietly debating a new concern: that the avalanche of sanctions directed at Moscow, which have gained speed faster than they imagined, is cornering President Vladimir V. Putin and may prompt him to lash out, perhaps expanding the conflict beyond Ukraine.

In Situation Room meetings in recent days, the issue has come up repeatedly, according to three officials. Mr. Putin’s tendency, American intelligence officials have told the White House and Congress, is to double down when he feels trapped by his own overreach. So they have described a series of possible reactions, ranging from indiscriminate shelling of Ukrainian cities to compensate for the early mistakes made by his invading force, to cyberattacks directed at the American financial system, to more nuclear threats and perhaps moves to take the war beyond Ukraine’s borders…

His strategy in coming weeks, some other American officials have warned in closed meetings since the crisis accelerated, could be to redirect the conflict toward Washington, hoping to distract from the Russian forces’ attacks on civilians in Ukraine and rouse a nationalistic response to the actions of a longtime adversary.

If Mr. Putin wants to strike at the American financial system, as Mr. Biden has struck at his, he has only one significant pathway in: his well-trained army of hackers, and an adjacent group of criminal ransomware operators, some of whom have publicly pledged to help him in his battle.