Despite the sharp uptick in cases he acknowledged and a US death toll that now exceeds 142,000, Trump declared that "it's all going to work out. And it is working out."

He suggested children do not transmit the coronavirus, though early evidence suggests children can and do. He attributed the recent rise in cases in part to racial justice protests, though early evidence suggests the protests did not cause a spike, and in part to migration from Mexico, though there is no evidence for this either.

Trump also claimed that he has done more for Black Americans than anyone else with the "possible exception" of President Abraham Lincoln. That is transparently ridiculous.

Here is a look at some of Trump's claims and the facts behind them.

Trump suggests Mexico to blame

In assigning blame for the uptick in coronavirus cases, Trump also suggested that Mexico was responsible, even though public health officials haven't publicly made this same accusation.

"Likely also contributing were also sharing a 2,000-mile border with Mexico, as we know very well, and cases are surging in Mexico, unfortunately," Trump said on Wednesday.

Referring to his proposed US-Mexico border wall, Trump added, "It was really meant for a different purpose, but it worked out very well for what we're doing right now and the pandemic."

Facts First: Trump didn't provide any evidence to back up his claims, and the nation's top public health officials aren't blaming Mexico for the US pandemic. Also, cases are spiking in states that don't share a border with Mexico -- like Florida, Louisiana and Idaho -- undercutting Trump's implication that border-crossers are bringing the disease into the US en masse. It's worth noting that the virus first flared in places such as Washington State, New York and New Jersey, thousands of miles away from the Mexican border.

After the briefing, CNN's Chief Medical Correspondent Sanjay Gupta said there isn't medical evidence supporting Trump's assertions. "I don't think there's any data specifically on Mexico," Gupta said. "We actually looked up to see if there was any data on that, and I didn't find any."

There is also a logic problem with Trump's comments. On one hand, he's blaming Mexico for the US spike. But he's also saying that the border barriers have successfully kept out the virus.

Kids transmitting the virus

During Wednesday's briefing, Trump continued to advocate for schools opening in the fall. In support of this he claimed that "a lot of people" say children "don't transmit" coronavirus.

"They don't catch it easily, they don't bring it home easily," Trump added. "And if they do catch it, they get better fast."

According to one recent study from the Korea Centers for Disease Control and Prevention, children between 10 and 19 years old may transmit coronavirus just as much as adults.

"Although the detection rate for contacts of preschool-aged children was lower, young children may show higher attack rates when the school closure ends, contributing to community transmission of Covid-19," the study said.

As a result, even though children appear to be affected less commonly or severely than adults, returning to school still poses certain risks.

Protests and the rise in cases

Trump said there were a "number" of causes for the recent spike in coronavirus cases. He cited some uncontroversial possible contributors, such as Americans returning to bars and increasing their travel.

The first cause he listed, though, was the racial justice protests that swept the country following the police killing of George Floyd in Minneapolis in late May.

"Cases started to rise among young Americans shortly after demonstrations...which presumably triggered a broader relaxation of mitigation nationwide," Trump said.

Obama and Chicago

CNN's Kaitlan Collins noted that in 2016 Trump said that it was President Barack Obama's fault that homicides were up in Chicago. She questioned Trump, "Why was it the President's fault then and not your fault now?"

Trump claimed that Obama "was invited in and he did a poor job. President Obama could've gone into Chicago. He couldn't have solved the problem and he didn't."

Since his early days in office, Trump has suggested sending the National Guard to curb gun violence in Chicago. Chicago's history with the National Guard is tumultuous, most notably during the 1968 Chicago riots and later at the 1968 Democratic National Convention.

Chicago wants a federal presence in the city

After Trump announced plans to send a "surge of federal law enforcement" to Chicago this week after the city experienced more gun violence, he claimed that Chicago will "want us to go in, full blast."

"I think in their own way they want us to go in, full blast. There will be a time when they're going to want us to go in full blast, but right now we are sending extra people to help. We are arresting a lot of people that have been very bad," the President said.

Facts First: This is an overstatement and needs context. The mayor of Chicago, who has a testy relationship with Trump, has cautiously welcomed federal law enforcement into the city to help combat its gun violence, but noted that federal agents were not welcome to "terrorize our residents."

But by Tuesday, Lightfoot cautiously embraced Trump's federal law enforcement to help combat Chicago's gun violence so long as the agents remain focused on gun violence.

Trump and Black Americans

But Trump's response to Biden's assertion was also wrong.

Facts First: While we give Trump lots of latitude to express opinions, this one is simply ridiculous even if he is only comparing himself to previous presidents and excluding other Black heroes. It's absurd to say Lincoln is a "possible" exception; emancipating the slaves was obviously more important for Black Americans than anything Trump has done. President Lyndon B. Johnson signed the 1964 Civil Rights Act and the 1965 Voting Rights Act, monumental bills whose impact dwarfed the impact of any legislation Trump has signed.

CNN's Andrea Kane contributed to this fact check.

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Fact check: Trump falsely suggests kids don't transmit coronavirus and that US case surge is due in part to protests and Mexican migration - CNN