King pointed to statements from the Biden camp to her CBS colleague Ed O'Keefe.
"You’re accused of delivering a low blow last night. What do you say to that?” King said.
Harris said her challenge of Biden was about "speaking the truth" and reiterated her respect for Biden, which she also emphasized in post-debate comments to Fox News' Peter Doocy.
"As I’ve said many times, I have a great deal of respect for Joe Biden. He’s served our country for many years in a noble way. But he and I disagree on that. It is a debate. This is a campaign where we should be discussing issues and there will be contrasts," she told King, emphasizing how personal the issue is for her.
"If segregationists had their way, I would not be a member of the United States Senate today, I would not be a top contender to be president of the United States," said Harris.
Asked whether Biden's civil rights record "effectively disqualifies" him from becoming president, Harris answered, "No, I think the voters will decide."