In an AP-NORC poll taken in mid-June, fewer than half of white respondents -- 39% -- believe that police violence against the public is either an extreme or very serious problem, compared with 80% of Black respondents.
Those numbers did show a shrinking of the gulf between the way white and Black Americans view the issue. The same poll was taken in the early stages of the Black Lives Matter movement in 2015, and then only 19% of white people said police violence was an extreme or serious problem, compared with 73% of Black people.
"It created this opening for white people," Battalora said of Floyd's killing. "But that's different from saying we 'get it.' That will be more of a process."
It remains to be seen whether the spectacle in recent days of white people locking hands to protect Black demonstrators from riot police, or taking part in the toppling of monuments to Confederate soldiers and slaveholders, represents a turning point.
"You have those historic moments where the nation can go one way or the other way," said Clayborne Carson, a civil rights scholar at Stanford University.
"But you just have to wonder -- why did it take so long?" said Carson, the founding director of the Martin Luther King Jr. Research and Education Institute and senior adviser on "Eyes on the Prize," the public television series on the civil rights movement. "It's not as if George Floyd was the first Black man to be killed by the police."
Carson was a student activist in the 1960s in Watts, then a heavily Black community. He saw firsthand how unrest over police brutality resulted in a backlash from anxious white people, many of whom flocked to "law and order" politicians like Ronald Reagan and Richard Nixon who promised to crack down on demonstrators.
"You want to hope that it's going to go in a more positive, progressive direction, but there's also a strong element in American history of riding the wave of the resentment toward people pushing for change," Carson said.
"That's always the political choice. Do you vote out of fear fueled by racism or do you vote out of hope that things will get better? But fear is powerful."
As a father raising two young boys in Dallas, a city with its own history of racial tension and fatal police violence, Ashmore, 38, said he's focused on making sure his sons don't grow up with a fear or suspicion of Black people.