In the early weeks of the Trump administration’s push to slash funding that colleges and universities rely on, grants and contracts had been cut and, in a few cases, researchers had been laid off.

In recent days, the fiscal pain has come to students.

At the University of Pennsylvania, administrators have asked departments in the School of Arts & Sciences, the university’s largest school, to cut incoming Ph.D. students. In some cases, that meant reneging on informal offers, according to Wendy Roth, a professor of sociology.

Her department had to decide which of the students would be “unaccepted.” Dr. Roth, chair of graduate education, was chosen to explain those decisions to them.

“Two of them, I would say, were extremely upset. One person was in tears,” she said. “It’s just the most terrible thing to get that kind of news when your plans are made.”

Since taking office, the Trump administration has issued orders that threaten to broadly undercut the financial foundation of university based research, including deep reductions in overhead cost reimbursements through the National Institutes of Health. Court challenges have paused some of the cuts, but universities are bracing for uncertainty. The University of Pennsylvania could face a $250 million hit in N.I.H. funding alone.

Members of the administration have cast the cuts as a way to reduce wasteful government spending, sometimes in political terms. Last month, Katie Miller, who is working with Elon Musk’s team to trim federal spending, said the cuts would end “liberal D.E.I. deans’ slush fund.”

In some cases, schools are pre-emptively cutting their expenses as a precautionary measure.

North Carolina State University announced on Feb. 14 that it was freezing most hiring. Stanford University announced on Feb. 26 that it was freezing staff hiring, citing “very significant risks” to the community. At the University of Louisville in Kentucky, President Kim Schatzel announced an “immediate pause” on faculty and staff hiring until July. She cited the potential loss of $20 to $23 million in N.I.H. research funding. Dozens of other schools have announced hiring freezes or “chills.”

Many of the cuts are now hitting graduate education, too, which is highly dependent on research grants, leaving students who had dreams of pursuing Ph.D.s with nowhere to go.

A graduate program in biological sciences at the University of California, San Diego, usually enrolls 25 new graduate students a year. This year, the number will be 17.

The reduction may seem small, but Kimberly Cooper, a biology professor, said the Trump cuts would ricochet through the university.

“I hate to sound fatalistic,” said Dr. Cooper, who specializes in the study of limb development. “But at this point I think they’re trying to break the academic enterprise. And cutting academic science has impacts on the educational mission of the entire university.”

At Penn, cuts to graduate programs were made across the board in the school’s 32 programs, professors said. The history department, for example, was asked to offer Ph.D. slots to only seven students, not the usual 17. In English, the normal cohort of 9 to 12 incoming students will be reduced to a maximum of six.

A letter signed by professors in 22 departments at Penn warned that the school’s decision would cause reputational damage.

Asked to comment, the university pointed to a statement signed by J. Larry Jameson, Penn’s interim president, posted on the school’s website, which noted that the cuts “represent an existential threat across our university and American higher education.”

Dr. Jameson said the school was pursuing “cost containment measures and new sources of revenue.” He added: “We will remain judicious, measured, deliberate and focused on sustaining our mission when determining any action.”

As the Trump administration vows to target schools over antisemitism and diversity initiatives, other programs that directly touch undergraduates, such as scholarships, could be affected, too, if the administration clears legal hurdles.

David Kazanjian, graduate chair of comparative literature at Penn, said the cuts to graduate students would reduce opportunities for undergraduates. With fewer graduate student teachers, class sizes may increase, for example.

The cost-cutting measures are taking effect across a variety of schools, from the Ivy League and large public research universities to smaller public schools. The administration’s decision to cap overhead reimbursements on National Institutes of Health grants to 15 percent could cut millions that schools have come to rely on to cover facilities and staff. The overhead rates normally vary depending on the grant recipients, but in some cases provide up to 60 percent of the grant in additional reimbursements.

Columbia University, which receives about $1.3 billion a year in N.I.H. funding, could lose up to $200 million a year from the formula change, according to one analysis by a group of university faculty and staff members and alumni called the Stand Columbia Society.

A graduate-student union at Columbia reported in a news release last month that university officials had proposed even more draconian cuts than Penn: eliminating up to 65 percent of incoming Ph.D. students in the School of Arts & Sciences. Following criticism, the cuts at Columbia were ultimately scaled back, and no firm numbers have been released.

The graduate workers at Columbia argued that there was no need for funding cuts, citing the university’s endowment, which grew to $14.9 billion at the close of 2024 from $13.6 billion in 2023. Yale, for example, one of the largest recipients of N.I.H. dollars, has announced that it would provide temporary funding from its own coffers for scholars.

A Columbia University official said that university endowments are generally restricted by purpose and in many cases could not be used to support Ph.D’s.

But this week, the Education Department said it would review all of Columbia’s federal contracts and grants, accusing the school of not doing enough to curb antisemitism on campus. The administration identified $51.4 million in contracts between Columbia and the federal government that could be subject to stop-work orders.

Schools with large endowments may also be a target of increased taxation. Endowments, generally accumulated with donor funds invested over decades, had largely been considered off limits for taxes because the universities operate as nonprofits.

But in 2017, during Mr. Trump’s first term, Republicans led a charge to impose a 1.4 percent excise tax on the investment income of large private university endowments. Now there are discussions of raising it to 14 percent, or even 21 percent.

The threatened N.I.H. cuts and the endowment tax comes on the heels of other major cutbacks at public land grant universities. Among the Trump administration’s first targets was a U.S. Agency for International Development program called “Feed the Future,” which funded 19 agricultural labs in 17 states. Many of those laboratories are now being shut down.

At U.C. San Diego, which was already facing state budget cuts, Dr. Cooper, the biology professor, said the fallout would have repercussions beyond universities if fewer students passed through their programs, and could affect entire sectors of the economy.

“The bigger issue in all this is that, this is our future biomedical work force,” she said.