Sen. Scott Brown, R-Mass., left, shakes hands with his Democratic challenger, Elizabeth Warren, right, on the set before their first debate as moderator Jon Keller, center, looks on, Thursday. (Michael Dwyer/AP)

The two candidates in the nation’s most high-profile Senate race met Thursday for their first debate — one in which Sen. Scott Brown (R-Mass.) portrayed himself as an antidote to Washington’s crippling partisanship, and Democratic challenger Elizabeth Warren cast herself as a champion against moneyed interests.

Both were on the attack in a clash that underscored their very different strategies. Warren, a Harvard Law School professor and first-time candidate, invoked national themes — that their race could determine whether the Senate remains in Democratic hands — and her desire to advance President Obama’s agenda.

Brown, on the other hand, did not mention the name of Mitt Romney, the former Massachusetts governor who is seeking to replace Obama in the White House. Instead, he focused on his opponent, whom he said is “obsessed with raising taxes,” charging that she would put taxpayer money “in her piggy bank so she can take it to Washington.”

Taxes were a major focus for both candidates. Brown said he would not raise them on anyone, while Warren contended that he was taking that stance to stave off higher levies on the wealthy.

“Where Senator Brown is always standing is right over there with the millionaires, with the billionaires,” Warren said.

The first six minutes of the hour-long debate, however, were dominated by a controversy that has dogged Warren — her claim that she is of Native American ancestry and the questions that Republicans have raised about whether that gave her an advantage in receiving prestigious faculty appointments.

“Character is important,” Brown said. “Professor Warren claimed she was a Native American, a person of color, and as you can see she is not.”

He again called upon her to release her personnel records and said: “I don’t know and neither do the viewers know whether she got ahead as a result of that checking of the box.”

Warren again insisted that her declared ancestry had nothing to do with her career advancement, adding: “What I really want this race to be about is about the issues, not about my family.”

The two also sparred over a number of gender-related issues, including Brown’s vote against Elena Kagan as a Supreme Court justice and his opposition to legislation that would require employers to justify discrepancies between how much they pay their male and female workers.

Brown said he voted against Kagan because he was concerned about her experience, not her gender, and that he had opposed the pay equity legislation because he feared it would be “an early Christmas present for plaintiffs lawyers.”

“He cannot back off from how he’s voted,” Warren said. “Women need someone they can count on, not some of the time, but all of the time.” That latter comment was one she repeated several times.

Brown, however, insisted that he has always been a champion of women and made numerous references to his wife and two daughters. “You should stop scaring women,” he said, more than once.

The debate, one of four that are scheduled, took place in a studio of WBZ-TV, the CBS affiliate in Boston, with no live audience. But hours before it began, hundreds of sign-waving supporters of both candidates lined the street outside.

Brown’s surprise victory in a January 2010 special election to fill the Senate seat of the late Edward M. Kennedy counts as one of the GOP’s greatest triumphs in recent years. It was an early warning of the rout that lay ahead for the Democrats in that year’s midterm election, and it deprived them of their filibuster-proof majority in the Senate.

But where two years ago Brown — then a little-known state senator — ran promising to be a roadblock to Obama’s agenda, he has portrayed himself in his re-election bid as a bridge between the two parties in gridlocked Washington. His challenge is to slip off his GOP label in a state where Democrats outnumber Republicans by roughly three to one, and where about half the electorate declares itself "unenrolled.”

Warren, on the other hand, began the race as an icon to liberals across the country. She gained a national reputation for the aggressive stance she took against Wall Street banks in setting up the Obama administration’s new federal Consumer Financial Protection Bureau. As a candidate, however, she has lacked a natural ease and personal warmth.

Brown arrived at the debate in the black GMC pickup that is the trademark of his regular-guy image and noted during the exchange that it had recently cost him more than $70 to fill it with gas.

Earlier in the day, there had been some drama over the question of whether Brown would even make it to the debate at all.

The Senate had been squabbling over a six-month spending bill, and Brown said that if there were late-night votes, he would skip the debate.

Senate Majority Leader Harry M. Reid (D-Nev.) — for whom winning back that long-time Democratic seat is a top priority — announced as a result that there would be no votes Thursday evening. “One of the senators who had a debate tonight doesn’t want to debate,” Reid said. “Well, he can’t use the Senate as an excuse.”

After the debate, Warren met with reporters, while Brown ducked out of the studio.

“This is a chance for me to be able to introduce myself to more of the voters of the commonwealth of Massachusetts,” she said. “It’s about them. It’s not about me.”