BOSTON—Rev. Jeff Brown knew his endorsement, along with backing from a slate of other prominent black faith leaders here, would be a boost to Elizabeth Warren in the fall of 2012, when she was in the home stretch of her first political campaign.

The incumbent, Republican Sen. Scott Brown, had been attacking Ms. Warren in television ads over her claims to Native American ancestry, for which she would later apologize. The race was rated a toss up by the nonpartisan Cook Political Report, despite Ms. Warren heavily outraising...