In September, Jason Doresky received a $10,000 direct deposit from the Education Department. It was a refund for payments he had made voluntarily on his federal student loans since March 2020, when the government told borrowers that they could stop paying temporarily because of the pandemic.

Three years later, those loans are still on hold — and Mr. Doresky, 31, who graduated from the University of Kansas in 2015, still has the money he received sitting in his savings account, untouched. He’s waiting to find out if he’ll have to send it back.

On Tuesday, the Supreme Court will hear arguments about President Biden’s plan to eliminate up to $20,000 in federal student loan debt for most borrowers, at an estimated cost of $400 billion. Mr. Biden’s plan, announced in August, has been blocked by legal challenges, preventing the government from canceling any debt for the 26 million borrowers who have applied for relief.

The White House insists its approach — which bypassed Congress and relies on a 2003 law, the HEROES Act, that allows the education secretary to grant relief in times of national emergency — is legally sound. The actions that Mr. Biden has directed Education Secretary Miguel Cardona to take “fall comfortably within the plain text of the act,” the administration argued in a legal filing to the court.

Challengers, including six Republican-led states, call it an abuse of executive authority that seeks “breathtaking and transformative power” by relying on “a tenuous and pretextual connection to a national emergency,” according to their legal brief.

Caught in limbo are millions of borrowers, like Mr. Doresky, who have swung between hope and despair as Mr. Biden’s relief plan was started and then halted. “To the people making these decisions, $10,000 is not a lot of money,” Mr. Doresky said. “But when it’s a big part of your actual net worth or savings, it really matters.”

More than two dozen advocacy groups plan to bus in hundreds of borrowers to rally outside the Supreme Court on Tuesday. The event has aligned labor unions, civil rights organizations and youth activists with groups as diverse as the Hip Hop Caucus and the National Council of Jewish Women.

Desiree Veney, a senior at Morgan State University in Baltimore and the vice president of her campus chapter of the National Association for the Advancement of Colored People, plans to hit the road before dawn to join the demonstration. A first-generation college student and the second-oldest of 10 siblings, Ms. Veney sees a clear racial-justice aspect to Mr. Biden’s plan. Black student loan borrowers typically leave school with $25,000 more in debt than white graduates, and carry the debt for years longer.

“It’s such a wide gap,” Ms. Veney said.

Mr. Biden’s plan would cancel $20,000 in debt for those, like her, who received Pell grants, which aid students from low-income families. That would wipe out nearly all of Ms. Veney’s undergraduate loans — making it easier for her to pursue the master’s and Ph.D. degrees she hopes to attain. She aims to become a therapist and work with families and troubled youths.

The president’s plan “would help reduce the racial wealth gap,” she said. “It would give not only me, but everyone, an opportunity to improve our financial security and lay a better foundation for upward economic mobility.”

Mr. Biden has cast his debt relief plan as an essential step in restarting a student-loan collection system that has been frozen for nearly three years. The hiatus began as a two-month pause initiated by President Donald J. Trump’s administration when the pandemic was ravaging the economy. Congress and Mr. Trump extended the hiatus three times, and Mr. Biden six more times, most recently in November. The president announced then that borrowers’ bills would resume 60 days after the court challenges to his relief plan were resolved or Sept. 1, whichever came sooner.

The piecemeal nature of the moratorium’s extensions — and the continued uncertainty about when people will actually have to start paying — has frustrated both borrowers and the companies that bill them on the government’s behalf. Nelnet, the largest federal loan servicer, laid off 350 newly hired employees last month, citing the likelihood that payments would remain paused for most of this year.

After such a long timeout, getting borrowers to resume paying bills that often total hundreds or thousands of dollars a month will be a “psychological hurdle,” acknowledged Richard Cordray, the chief operating officer of the Education Department’s Federal Student Aid office.

“We can expect that many, many borrowers will not be eager to return to repayment when they have been led to believe, or even to hope, that was never going to happen,” Mr. Cordray said in a speech at an industry conference — back in September 2021.

The Education Department has used the long pause to try to clean up some of the $1.6 trillion federal student loan system’s biggest failings. A one-time waiver to rules that had become Kafkaesque in their complexity let hundreds of thousands of public service workers get $14 billion in loans forgiven. One million borrowers who attended schools that defrauded them had nearly $15 billion in debt eliminated, and loans were automatically discharged for hundreds of thousands of permanently disabled borrowers.

More is in the works. The Education Department is preparing a new income-linked repayment plan that would sharply reduce payments for many who borrow for undergraduate studies. It is working on a complex waiver program, to be carried out this summer, that will retroactively credit millions of borrowers on income-driven plans with additional payments toward loan forgiveness. The agency also plans a “fresh start” amnesty for the seven million borrowers — nearly one in every five people with payments due — who have defaulted on their loans.

All of that becomes easier if the Supreme Court allows Mr. Biden’s debt cancellation plan to proceed. The White House estimates that nearly 90 percent of the nation’s 45 million student loan borrowers would qualify for some relief, and that 18 million would have their debts fully canceled.

The administration’s legal case for wiping out tens of millions of borrowers’ loans focuses on the pandemic’s lingering effects on the finances of many households. Without debt cancellation, the White House fears many borrowers will be walloped when payments resume, leading to what the Education Department projected could be a “historically large increase” in defaults and delinquencies.

“The borrowers most likely to struggle disproportionately come from lower-income households — the families least prepared to weather the public health and economic crises that gripped the country in 2020,” Mike Pierce, the executive director of the Student Borrower Protection Center, said Friday on a call that the White House had arranged for reporters.

Critics see that argument as a fig-leaf justification by Mr. Biden to achieve through executive order what he has been unable to accomplish legislatively: mass student debt cancellation. “Other Americans will have to pick up the tab, to the tune of over $2,500 per taxpayer,” dozens of Republican senators wrote in an amicus brief submitted to the Supreme Court.

More than half the House’s Republicans joined in their own brief, which warned the Supreme Court that if it allowed Mr. Biden’s plan to proceed, “it is only a matter of when, not if,” an education secretary would again invoke such broad student-debt cancellation powers.

That would be a welcome outcome for Kristin McGuire, the executive director of Young Invincibles, a young-adult economic advocacy group that is helping to organize the rally on Tuesday.

A first-generation college student, Ms. McGuire defaulted on her loans soon after she graduated in 2005. She carried enormous shame and guilt, she said, viewing it as a personal failing — until she began working as an activist and discovered how common her story was.

“What I realized is that this is an issue that’s impacting millions of people. It’s not an isolated incident,” she said. “We’ve sat here and we’ve watched as corporations get bailed out and get debt canceled year after year, every time we have any sort of economic downturn. I really believe it’s time for the people to be able to access that type of benefit as well.”