Harris, the 54-year-old junior senator from California, picked up substantial backing, meanwhile, from Democrats and Democratic-leaning voters in the polls conducted by Quinnipiac University, CNN and Politico/Morning Consult.
In another measure, intended participation is high: Seventy-two percent of leaned Democrats say they're certain to vote in their state's primary or caucus.
Sen. Bernie Sanders also (I-Vt.) also saw his support drop by 4 percent after the debates.
But they appeared to be looking elsewhere after Kamala Harris, a USA senator from California also seeking the presidency, criticised Biden for opposing mandatory busing to integrate schools in the 1970s and for his cooperation with segregationists while he was a young senator. Harris got 16 percent in the poll, and Warren (D-MA) isn't far behind at 13 percent. The remaining candidates have 3 percent or less, according to the survey. According to the poll, four out of 10 respondents indicated they thought he did worse during the debate than expected.
"Harris also essentially catches Biden among black Democratic voters, a historically strong voting bloc for Biden, with Biden at 31 per cent and Harris at 27 percent", the opinion poll said. Sanders and Warren are tied with 15 percent, while no other candidate reaches double digits.
United Kingdom support for Hong Kong ‘freedoms is unwavering’, says Hunt
Police estimated 190,000 people joined the peaceful march, the third major one in as many weeks. Participants were shouting " Carrie Lam step down, Withdraw the evil law".
Harris's exchange with Biden on racial discrimination was seen as a standout moment during the two debates among the two dozen candidates seeking to become the Democratic standard-bearer against Republican President Donald Trump in November 2020.
At the same time, the poll reveals Former Vice President Joe Biden's lead has since narrowed.
The Quinnipiac University poll was conducted June 28-July 1 among 554 Democrats and Democratic-leaning voters and has a margin of error of five percentage points.
The Indian-origin Senator, whose mother was born in Tamil Nadu and father was an African-American from Jamaica, in January launched her campaign for the presidential election. Challenging the former vice president on his civil rights record, Harris talked about a little girl who had to be bused to a newly-desegregated school.
In the average of upwards of 20 polls tracked and aggregated by RealClearPolitics, Harris is in the third position, with Sanders still holding the No 2 slot, only by 1.4 points.
Ahead of the debate, Biden had come under harsh criticism for boasting about his ability to form working relationships in past decades with segregationist Democratic Sens.