"American investment in education is a promise to students and their families. If schools aren't going to reopen and not fulfill that promise, they shouldn't get the funds, and give it to the families to decide to go to a school that is going to meet that promise," DeVos told "Fox News Sunday."
"There's going to be the exception to the rule, but the rule should be that kids go back to school this fall," DeVos said Sunday, using language similar to the president. "And where there are little flare-ups or hot spots, that can be dealt with on a school by school or a case by case basis."
DeVos didn't say under which authority she and Trump would have to cut off school budgets.
While the administration threatens to slash funding, the School Superintendents Association has estimated necessary protective measures to keep schools safe this fall would cost an average of about $1.8 million per school district. There are roughly 13,598 regular school districts in the U.S.
Asked about the DeVos demand that schools reopen five days a week, Monday, Miami Mayor Francis Suarez told ABC's "Good Morning America" he has "no idea" whether kids will go back to school in a matter of weeks as cases in the state surge.
"Our superintendent is the one that runs our school systems and he has indicated that he's not going to put our children at risk," he said. "The education commissioner of the state of Florida has mandated schools be open but I'm not sure our superintendent is in agreement with that and certainly, you know, not if it poses a risk to our children or to the parent or those teaching."
Suarez, a Republican, said he hasn't ruled a stay-at-home order out. Florida GOP Gov. Ron DeSantis, meanwhile, a Trump ally, said last week: "If you can do Walmart," then "we absolutely can do the schools."
Trying to smooth over the conflict with Florida and with other state and local officials, White House press secretary Kayleigh McEnany claimed in an interview Monday on "Fox & Friends" that "We leave it to localities as to exactly what guidelines work, because guidelines in a state like North Dakota need to look different than a locality like Miami.
In California, where cases are on the rise, the superintendent of the Los Angeles Unified School District announced Monday LA public school students won't have in-person classes when the school year starts in August.
"The health and safety of all in the school community is not something we can compromise," said Austin Beutner in a statement. "Children need to be in school to get the best possible education. The right way to reopen schools is to make sure there is a robust system of testing and contact tracing to mitigate the risk for all in the school community."
Responding to DeVos' comments Sunday, Randi Weingarten, president of the American Federation of Teachers, tweeted that Trump and DeVos are not putting the safety of children and teachers first and criticized their lack of planning and resources offered as some schools are set to open in a month or even before.
"Their goal isn't safety, it's politics," she tweeted. "It's what they think is good for @realDonaldTrump, not what's good for the country."
Weingarten also tweeted out a report from the Kaiser Institute published Friday found that one in four teachers have a condition that puts them at higher risk of serious illness from coronavirus.economic
The president's top economic adviser, Larry Kudlow, on Monday doubled down on saying it's "not that hard" to return to school amid the pandemic.
"It's not to say they are burdens, and can't we put the best minds together and can't we figure out masking?" he said in an interview with Fox News. "This is not so difficult."
Rep. Ayanna Pressley, D-Mass., also took to Twitter to criticize DeVos, who has no experience as an educator, for having "no plan."
"I wouldn't trust you to care for a house plant let alone my child," she wrote.
Rep. Jahana Hayes, D-Conn., a former national teacher of the year, told NBC she hopes DeVos defers to "the people who know best," as she said the education secretary is "not advocating for students and teachers, she is not holding her title and her responsibility to speak on behalf of millions of teachers and students that she's responsible for."
The Centers for Disease Control and Prevention has released guidelines for reopening amid coronavirus concerns, advising schools to keep desks placed six feet apart, to close communal areas like cafeterias and playgrounds and to have children use face coverings and schools -- but they've come under fire from President Trump.
On Wednesday he criticized them as "very tough" and "expensive." He tweeted Twitter Friday that "schools must be open in the Fall," arguing that virtual learning is "TERRIBLE" compared to in-person.
Falling in line, even CDC Director Dr. Robert Redfield, after the president's criticisms, told ABC's "Good Morning America" the CDC will release "additional information to help the schools be able to use the guidance that we put forward."
"The president said today we just don't want the guidance to be too tough," Vice President Mike Pence said during a coronavirus task force briefing Wednesday. "That's the reason why, next week, CDC is going to be issuing a new set of tools, five different documents that will be giving even more clarity on the guidance going forward."
In the same briefing White House coronavirus response coordinator Dr. Deborah Birx acknowledged "the lowest tested portion [of the population] is the under 10-year-olds."
Though the Trump administration is downplaying the risks of sending children back to school, internal CDC documents obtained by the New York Times warn that fully reopening schools and universities would create the "highest risk" of spreading the coronavirus.
And the American Academy of Pediatrics, whose guidance the Trump administration has cited to support its demands, made clear Friday that while in-person school provides crucial benefits to children, "Public health agencies must make recommendations based on evidence, not politics."
The AAP statement aimed at Trump and DeVos joined with three other groups -- the American Federation of Teachers, the second-largest teachers union in the country; the National Education Association, the largest union in the country; and AASA, the School Superintendents Association -- and said any threat to cut funding was "a misguided approach."
"Science should drive decision-making on safely reopening schools. Public health agencies must make recommendations based on evidence, not politics," the statement said. "We call on Congress and the administration to provide the federal resources needed to ensure that inadequate funding does not stand in the way of safely educating and caring for children in our schools."
The Trump administration had repeatedly cited an AAP statement from last month saying the organization "strongly advocates that all policy considerations for the coming school year should start with a goal of having students physically present in school."
The AAP guidance also came up at a White House school-opening roundtable on July 7 led by President Trump. Pence highlighted the presence of AAP president Dr. Sally Goza.
"But as the American Academy of Pediatrics, so well represented here today, recently reflected, there are -- there are social costs, emotional costs, and even physical costs to our children across this country that we spoke with the governors today," Pence said.
Goza, speaking before Trump and Pence, emphasized in her remarks, "returning to school must be done safely."
"Reopening schools in a way that maximizes safety, learning, and the well-being of children will clearly require new investments in our schools. We urge you to ensure that schools receive the resources necessary so that funding does not stand in the way of keeping our children safe or present at school," she said, a month before Trump fired off new threats to cut funds.
The push to reopen schools comes as new coronavirus cases are spiking in the U.S. Sun Belt. Florida on Sunday reported more than 15,000 new cases, making it one of the world's biggest hot spots and setting an all-time record for any state.
District leaders and school boards across the country are grappling with the decision to reopen as politics invades the debate.
McEnany also accused House Speaker Nancy Pelosi of "messing with our children," after Pelosi told CNN's "State of the Union" Sunday, when asked to react to the DeVos comments, that "The president and his administration are messing with the health of our children."
"I think what we heard from the secretary was malfeasance and dereliction of duty. This is appalling. They're messing, they're messing -- the president and his administration are messing with the health of our children," Pelosi said. "If there are CDC guidelines, they should be requirements."
Testing czar Adm. Brett Giroir played down the risks to children on ABC's "This Week" with George Stephanopoulos, pointing to other countries that have not seen the case counts the U.S. has experienced.
"We know from other countries, particularly young children do not seem to spread the virus. We know they don't get sick," he said, though he emphasized getting the virus "under control" is the top priority, "then we can think about how we put children back in the classroom."
While DeVos has not offered a plan of her own, she has criticized other "hybrid plans" some schools have announced plans to bring students back for only a few days a week.
During a call with governors last week, DeVos slammed plans by Virginia's Fairfax County Public Schools to have families make the choice between fully remote instruction or two days a week at school.
"A choice of two days per week in the classroom is not a choice at all," DeVos said, according to audio of the call obtained by The Associated Press. "Ultimately, it's not a matter of if schools need to open, it's a matter of how. Schools must reopen, they must be fully operational. And how that happens is best left to education and community leaders."
ABC News' Ben Gittleson, Jordyn Phelps and Elizabeth Thomas contributed to this report.