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He said that likely would run afoul of the Constitution’s grant of powers to the president in Article 2.

The 2011 killing in Yemen of Anwar al-Awlaki, an American citizen tied to an al Qaeda offshoot, helped push the drone execution program into the public eye — though the administration regularly declined to confirm its existence even as recently as last month.

But NBC News last month obtained a Justice Department memo explaining the legal justification for targeted killings. At the same time, Mr. Obama has been trying to reconstitute his second-term Cabinet, and those nominations have become leverage for senators, who have demanded information in return for agreeing to hold confirmation votes.

The killings overseas have raised questions about what would be allowed on the homeland.

Mr. Paul described the legal situation as one in which one person — the president — holds the power to be the accuser, the judge and the executioner, since terrorist-designation proceedings are all contained within the executive branch and conducted generally in secret.

“Are we so afraid of terrorism, are we so afraid of terrorists that we’re willing to just throw out our rights and freedom?” he said.

But Mr. Holder, speaking to the Judiciary Committee, disputed Mr. Paul’s scenario of someone sitting in a cafe in Kentucky being executed by a drone attack. He said the government cannot use lethal force against an American citizen on U.S. soil unless that person is deemed to be an imminent threat to security. He said that goes for normal law enforcement and the military, even in time of war.

Amid the back-and-forth, Mr. Brennan’s nomination still awaits action.

Senate Majority Leader Harry Reid, Nevada Democrat, had hoped to schedule a vote for Wednesday afternoon, but Mr. Paul’s filibuster foiled that.

Mr. Reid said he now wants to vote Thursday, but Republicans could stretch that out through the weekend if they use all parliamentary tactics and time available to them.

Mr. Brennan’s nomination cleared the Senate intelligence committee on a 12-3 vote Tuesday, but the full Senate had just begun its debate when Mr. Paul grabbed the floor at 11:47 a.m. Wednesday and refused to relinquish it until almost 13 hours later, after midnight on Wednesday.

“I rise today to begin to filibuster John Brennan’s nomination for the CIA. I will speak until I can no longer speak,” he began.