He added, "And so I want to thank Harvard, I want to thank Stanford and I want to thank the other companies. Any case, it's broken differently between the colleges and companies, but I want to thank the companies and other great universities."

The lion’s share of the relief money — more than 70 percent — is actually bound for public universities, according to a POLITICO analysis of Education Department data. Public universities overall are set to receive nearly $9 billion of the funding; private non-profit schools are set to receive nearly $2.5 billion; and more than $1 billion targets for-profit colleges. Public schools are bracing for the possibility that state legislatures in the coming months will cut funding for higher education amid drastic drops in state revenue.

But the prospect of colleges with massive endowments — Harvard’s is more than $40 billion — lining up for the money brought blowback from the administration, which also has been tussling with colleges in recent days over the slow rollout of emergency funds.

Stanford's endowment is $27.7 billion, while Princeton's is $26 billion, Yale's is $30.3 billion, MIT's is $17.5 billion, Notre Dame's is $11.2 billion and Rice's is $6.4 billion, according to fiscal 2019 figures from the National Association of College and University Business Officers and TIAA.

At least two Senate Republicans — Ted Cruz and Martha McSally — called on Harvard to forfeit its share of the money.

DeVos said in her statement that “wealthy institutions that do not primarily serve low-income students do not need or deserve additional taxpayer funds. This is common sense.”

Most of the nearly $14 billion in higher education funding under the CARES Act is allocated to colleges and universities based on a formula in the law. Colleges are entitled to a share of the funding based on the number of students they enroll, heavily weighted toward low-income Pell Grant recipients.

Top recipients of the stimulus cash include public institutions like Arizona State University ($63.5 million); Penn State ($55 million); Rutgers ($54 million); University of Central Florida ($51 million) and Miami Dade College ($49 million).

Colleges are required to use at least half of their share of the stimulus funding to award emergency cash grants directly to their students to help cover expenses like food, housing and child care. The rest can go to the institutions, with some restrictions, such as not paying for salaries or bonuses of senior administrators or executives.

The Trump administration this week issued new guidance on how colleges could use the stimulus money. The Education Department forbade for-profit colleges from using it for stock buybacks or shareholder dividends. The department also barred undocumented students, including DACA recipients, from accessing the emergency cash assistance.

The Trump administration is also now looking into whether a university’s share of stimulus money can be sent to another college if it is returned or never claimed. Education Department officials said they believe they can redistribute the money, a department official told POLITICO on Wednesday.

In order to access the stimulus bill funding, colleges and universities must sign an agreement affirming that they will properly use the money. As of Tuesday, about 50 percent of colleges had submitted that paperwork to access the student aid portion of the funding.

Stanford announced Monday that it had contacted the Education Department to rescind its request for relief funds, saying it wanted to keep the money available for smaller colleges.

While the university is expected to take a financial hit, “we realize that this crisis represents an existential threat for many of the smaller colleges and universities that are such a critical part of the fabric of higher learning in the United States,” said E.J. Miranda, a Stanford spokesperson.

“We believe strongly in the importance of keeping these institutions viable in order to provide access to higher education for as many students as possible, and we had concluded that this should be a priority,” he continued.