“Mostly we protect people from criminals, but sometimes we protect them from an overreaching government,” said Brad Rogers, the sheriff of Elkhart County, Ind. He added: “I’m answerable to the people. I have a face and a name. Try asking the federal government for a face and a name.”

The apotheosis of the idea that federal and state law is subordinate to local authority is Joe Arpaio, the former Arizona sheriff who earned notoriety for his aggressive pursuit of unauthorized Latino immigrants. After the 2012 school massacre in Newtown, Conn., hundreds of sheriffs allied with Mr. Arpaio signed a pledge not to enforce the Obama administration’s gun-control proposals.

Ultimately, Mr. Arpaio was convicted of contempt for defying a federal judge’s order to stop violating immigrants’ constitutional rights. But Mr. Trump pardoned him over the summer, seemingly endorsing his view of local authority. Indeed, the Trump administration has instructed sheriffs to disregard federal law and detain undocumented immigrant suspects longer than a number of federal judges have said is constitutionally allowed. And when the president announced this month that he was drastically shrinking two national monuments in Utah, he cast the decision in terms of protecting citizens from “federal overreach.”

Sheriff Franklin is ideologically aligned with many conservative causes, and during the 2016 presidential race had a featured role in a national advertising campaign where sheriffs called for tougher border security. “Lives are depending on it,” she said on camera.

In two interviews with The Times, the sheriff said she had done nothing illegal and had not violated anyone’s civil rights. “I have worked my tail off to try to do the right thing and make the best decisions that I can make,” she said.

She said she had tried to make her agency more accountable, and added, “Since I have taken office, I have attempted to train these deputies, to equip them, to manage them in the piddly little budget that I’ve been given.” As for the federal inquiry, the sheriff said, “The F.B.I. has not informed me of any such investigation.”

The sheriff makes no apologies for her belief that voters and the state constitution allow her to carry out her own vision of law enforcement. “I run it based on what the public wants or likes,” she said.