WASHINGTON — Confronted with a vast cyberattack believed to have been carried out by Russia, the Trump administration is suddenly reviving an old idea: Strip the general who leads the United States Cyber Command of his second title as the director of the National Security Agency, the country’s largest spy operation.

The idea has been kicking around Washington for years, and the intelligence world has hotly debated its merits. But a decision has always been put off because Cyber Command, the decade-old organization that leads the military’s offensive and defensive operations around the world, remains heavily dependent on intelligence provided by the N.S.A., the 68-year-old code-breaking agency.

As the government grapples with a vast hack, the Pentagon is weighing whether to separate management of the National Security Agency from the United States Cyber Command.

But when the idea was revived in recent days with a recommendation en route to the chairman of the Joint Chiefs, Gen. Mark A. Milley, for action before President Trump leaves office next month, it led to a firestorm of protest on Capitol Hill. Democrats and Republicans alike say that the two institutions are too intertwined to be managed separately and that any unilateral action by the administration to change the current structure would violate legal requirements for extensive assessments before altering it.

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