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“You should stop scaring women, professor, because I’ve been fighting for women since I was six years old,” he said.

Even as both candidates raise massive amounts of money behind the scenes, they’re also trying to appear before voters as the populist candidate.

They spent the first part of the debate wrangling over taxes, with each candidate sticking to positions they’ve already laid out: Mrs. Warren supports repealing the Bush tax cuts for those earning more than $250,000, while Mr. Brown has said he won’t support any tax increases, period.

Along with other Republicans in Congress, Mr. Brown has refused to support plans proposed by Democrats to extend the tax cuts beyond this year for the middle and lower classes only. Mrs. Warren seized on that, saying he’s willing to put middle-class tax cuts at risk as he protects wealthy Americans.

“He has just said he’ll defend the top 2 percent or top 3 percent, and he will hold the other 98 percent of families hostage,” she said.