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While she is hardly a conservative, Ms. Klobuchar has distinguished herself in the campaign by breaking from the new liberal orthodoxy that has dominated the primary.

She does not favor a “Medicare for all” health care system, preferring a more graduated approach; she has called the Green New Deal “aspirational”; and she has said the country cannot afford to fund free tuition for students at public colleges and universities. During her Fox News appearance, Ms. Klobuchar said she backed legal marijuana, but unlike many of her rivals would leave the decision to individual states rather than endorsing federal legalization.

When asked about Attorney General William P. Barr, Ms. Klobuchar backed the recommendation by the House Judiciary Committee to hold him in contempt of Congress for failing to turn over Robert S. Mueller III’s unredacted report about whether the Trump campaign conspired with Russia to undermine the 2016 presidential election, and if President Trump obstructed justice. She declined to answer whether Mr. Barr should face jail time.

“He should come before the House,” she said. “I think you’re going to see a lot of pushback and subpoenas, and I think that this administration has to take this seriously. They have to answer the people’s call.”

For Ms. Klobuchar, the event was an opportunity to reach a broader audience and build support beyond the Democratic base. Since she started her campaign in February, Ms. Klobuchar has struggled to break 5 percent in polling of early primary states. Former Vice President Joseph R. Biden Jr.’s entrance into the race further complicates her path, as he travels the country offering a similar appeal — that he could win back the Rust Belt voters who cost Hillary Clinton the 2016 election.