In a rare joint appearance, Democratic U.S. Sen. Amy Klobuchar and her Republican challenger, state Rep. Kurt Bills, jousted Tuesday at a Duluth debate over who rightly owns the mantle of bipartisan cooperation.

Backing off his previous adoption of conservative Republican budget plans, Bills said he was looking for "a great compromise" to settle the country's budget problems. Laying aside her record of voting with Democrats on the vast majority of measures in the past six years, Klobuchar said she has made her mark by finding areas of agreement with Republicans.

"Courage in the next few years is not going to be standing alone in the middle of a great debate giving a speech by yourself," she said. "Courage is whether you're willing to stand next to someone who you don't always agree with for the betterment of this country."

Bills, who has struggled to make himself known to vast swaths of the state, sought to appeal to voters by promising he would vote for a compromise on a federal budget solution even if it includes raising taxes.

"Even though I am staunch conservative, when it comes time to vote ... I will make that vote," said Bills, a freshman legislator from Rosemount making his first run at statewide office. At an event on Monday, Bills went so far as to offer "a verbal or physical confrontation with Grover Norquist," the leader of the unwaveringly anti-tax Americans for Tax Reform, to support compromise.

Bills said the broad income tax cuts passed under President George W. Bush were "terrible economic policy," and backed a "flat, fair, progressive tax system." Bills said he also would be willing to drop his call to eliminate the U.S. Department of Education if it would advance a Senate compromise.

"Instead of ending the Department of Education, let's zero-base the budget out," Bills said. Such a plan would rewrite the agency's budget from scratch, assessing each program before funding it.

Bills also dismissed Klobuchar's work on a federal debt commission. "We already have a debt commission," Bills said. "It's called Congress."

Klobuchar defended the work of the bipartisan commission.

"I don't think that debt commission is something silly, that's a piece of paper that's sitting on the wall," said Klobuchar who is working with Republicans on a framework to pay the country's debt.

"It is actually something that people are looking at for guidance of how we move forward."

Klobuchar said she would support increasing taxes on those earning more than $250,000 a year and slashing the federal budget to help whittle the federal debt.

"We are going to have to make some spending cuts. It's also about revenue," she said.

Tuesday's debate was tame compared with last month's feisty State Fair debate, with Klobuchar and Bills bantering on Tuesday morning before the event and with Bills wishing Klobuchar "a wonderful day" as the event concluded.

For Klobuchar, it was a day on friendly turf. She won 71 percent of the vote in Duluth six years ago and peppered her debate talk with northern Minnesota name-drops from her grandfather's work in the area's mines to her Senate work to help the city recover from this summer's floods.

"Things have not been easy up here, but you have never given up," Klobuchar told the crowd.

The moderators helped Klobuchar with that case. In his first question to Bills, Duluth News Tribune Editorial Page Editor Chuck Frederick thanked Bills for "being willing to come up here, to what traditionally has long been a stronghold for a popular senator."

Klobuchar and Bills will meet at least once more -- two days before the election -- in a debate sponsored by Minnesota Public Radio.

Rachel E. Stassen-Berger • Twitter: @rachelsb