President Obama, Michelle Obama and Dallas Mayor Mike Rawlings sing during a July 12 memorial service for multiple police officers killed in Dallas. (Carlo Allegri/Reuters)

Over two days, both President Obama and the man who hopes to replace him offered their assessments of the state of racial tensions in America. Both statements overlap in fascinating ways with partisanship, public perceptions and raw politics.

First was Donald Trump. After his speech about veterans Monday, he sat down for an interview with the Virginian-Pilot, during which the recent tensions between police and Black Lives Matter protesters arose. This was their exchange, as transcribed by CBS's Sopan Deb.

INTERVIEWER: How big is racism in this country?

TRUMP: I think it's a bigger problem than people understand. I think it's far bigger than President Obama wants to admit. I mean, he doesn't want to admit it — it's taking place during his administration. I mean, when you have 11 cities absolutely ready to blow up over the last three or four days. ... And it could very well get worse.

"I think it's far bigger than President Obama wants to admit" is a telling line, particularly given Obama's mention of it during his speech in Dallas on Tuesday, during a memorial service for the five police officers slain in that city over the weekend.

"Race relations have improved dramatically in my lifetime," Obama said. "Those who deny it are dishonoring the struggles that helped us achieve that progress. But America, we know that bias remains."

Those two statements, Trump's and Obama's, aren't necessarily in conflict. Obama is noting that since he's been alive — since 1961, shortly before the passage of the Civil Rights Act — the United States has gone from having legally segregated facilities to having a broadly integrated society. A society in which, for example, black Americans and white Americans vote at equal rates and, in 2008, we elected our first black president.

What's different is what they highlight. Trump focuses on the increase in racial tension of late, just as, on Tuesday morning, Trump warned about a spike in crime. His goal is to portray the situation as getting worse, and himself as the outsider who can fix the problem.

Crime isn't going up, but there is a broad perception that racial tensions have worsened. Gallup has asked Americans for their perceptions of race relations since 2001. There was a slight decrease from 2001 to 2010 in those who reported that they are worried "a great deal" about race relations, and then a big jump from 2014 to 2016. That period, it's important to note, overlaps with the rise of the Black Lives Matter movement and the focus on police treatment toward black civilians.

While every demographic group is now more worried about race relations than they were three years ago, the biggest increases in concern haven't been among the Republicans and white Americans who are more likely support Donald Trump. The biggest increases have been among black and liberal Americans. More than half of blacks now say they worry a great deal about race relations.

The data suggest that black Americans are more likely to be concerned about race relations than white ones, the inverse of what we heard from Trump and Obama. But there have been big jumps among Republicans and white voters, which Trump, with his comments, is tapping into. It's likely that things like Black Lives Matter are influencing both of those changes in different ways, with many black Americans tending to sympathize with the idea of police mistreatment and many whites seeing the movement as divisive. Trump is capturing the sentiment of that latter group with the hyperbolic suggestion that 11 cities are "ready to blow up."

Obama's remarks, on the other hand, are trying to tamp concerns down, reminding listeners that things have been much worse. It's the difference between being president and trying to get elected president. Obama wants to keep people calm. Trump wants to spur them to action in November.