WATCH: Psaki reacts to Supreme Court blocking Biden’s vaccine mandate on private businesses

Psaki said that Biden would be issuing a statement, and that the Supreme Court did not strike down the mandate for health care workers, but upheld that mandate, saying that the administration would be enforcing that.

The Supreme Court's ruled that the mandate for workers was not constitutional. The majority opinion read in part that "OSHA has never before imposed such a mandate. Nor has Congress. Indeed, although Congress has enacted significant legislation addressing the COVID–19 pandemic, it has declined to enact any measure similar to what OSHA has promulgated here."

Psaki spoke to the "good news" that health care workers would be required to be vaccinated, and that this mandate would cover some "17 million health care workers at 76,000 Medical facilities."

"The Supreme Court's decision on the OSHA mandate," she said, "essentially means that in this pandemic it is up to individual employers to determine whether their workplaces will be safe for employees and whether their businesses will be safe for consumers."

As such, Biden will continue to urge corporations to enforce mandates on their own. "So President Biden, you'll see this in his statement, will be calling on businesses to immediately join us for those who have already stepped up, including one third of Fortune 500 companies to institute vaccine requirements to protect their workers, customers and communities," she said.

"We have to keep working together in order to get this done to save more lives," she said. She touted a ramp-up in testing as well, and claimed that most Americans support vaccine mandates, despite it having been ruled unconstitutional.

Psaki also said, in response to questions on the Supreme Court decision, that the reason the administration undertook the mandate was that it "would help more people get vaccinated." She cited statistics that more than 80 percent of Americans had received one dose of vaccine so far.