WASHINGTON — The Supreme Court will hear arguments on Tuesday over the legality of one of the most ambitious and expensive executive actions in the nation’s history: the Biden administration’s plan to wipe out more than $400 billion in student debt because of the coronavirus pandemic.

The administration faces a conservative court that has been hostile to other programs justified by the pandemic and insistent that government initiatives with major political and economic consequences be clearly authorized by Congress.

The law the administration relies on, the Higher Education Relief Opportunities for Students Act of 2003, usually called the HEROES Act, gives the secretary of education the power to “waive or modify any statutory or regulatory provision” to protect borrowers affected by “a war or other military operation or national emergency.”

In March 2020, President Donald J. Trump declared that the coronavirus pandemic was a national emergency, and his administration invoked the HEROES Act to pause student loan repayment requirements and to suspend the accrual of interest.

The Biden administration followed suit. As of April, the payment pause has cost the government more than $100 billion, according to the Government Accountability Office.

In August, the administration said it planned to switch gears, ending the repayment pause but forgiving $10,000 in debt for individuals earning less than $125,000 per year, or $250,000 per household, and $20,000 for those who received Pell grants for low-income families. The nonpartisan Congressional Budget Office has estimated the plan’s price tag at $400 billion.

In separate cases, six Republican-led states — Nebraska, Missouri, Arkansas, Iowa, Kansas and South Carolina — and two individuals sued to stop the new plan.

The first question in both cases is whether the plaintiffs have suffered the sort of direct and concrete injury that gives them standing to sue.

The states lost on that ground before Judge Henry E. Autrey of the Federal District Court in St. Louis, who was appointed by President George W. Bush.

“While plaintiffs present important and significant challenges to the debt relief plan,” Judge Autrey wrote, “the current plaintiffs are unable to proceed to the resolution of these challenges.”

A three-judge panel of the U.S. Court of Appeals for Eighth Circuit blocked that ruling. Two of its three members — Judges Ralph R. Erickson and Leonard S. Grasz — were appointed by Mr. Trump. The third, Judge Bobby E. Shepherd, was appointed by Mr. Bush.

The appeals court focused on the possibility that a nonprofit entity that services federal loans, the Missouri Higher Education Loan Authority, might fail to make payments to Missouri if the program were allowed to proceed. In the Supreme Court, the states are also arguing that the loan forgiveness program would cause their tax revenues to fall.

The case brought by the two borrowers, Myra Brown and Alexander Taylor, also raised questions about standing. Ms. Brown is ineligible for relief under the plan because her loans are held by commercial entities rather than the government, while Mr. Taylor is eligible for $10,000 rather than $20,000 because he did not receive a Pell grant.

A trial court ruled that they had standing to sue because they had been deprived of the opportunity to urge the administration to expand the plan to provide greater debt relief.

In its Supreme Court brief, the administration argued that none of the challengers have standing. The states’ asserted injuries, the brief said, were speculative or self-inflicted.

The individual borrowers, the brief added, would be no better off if they prevailed. A ruling in their favor “would not grant Brown and Taylor the additional debt relief they say they desire; rather, it would mean that nobody gets any debt relief at all,” the brief said.

If the Supreme Court rules that at least one plaintiff has standing, it will address whether the debt forgiveness plan is lawful.

The court has increasingly insisted on clear grants of congressional authority in cases with significant political or economic consequences. It calls this requirement the “major questions doctrine.”

In June, the court invoked the doctrine in a decision that curtailed the Environmental Protection Agency’s power to address climate change. Without “clear congressional authorization,” the court said, the agency could not act.

Chief Justice John G. Roberts Jr., employing the phrase for the first time in a majority opinion, said it applied in cases of unusual significance and was meant to address “a particular and recurring problem: agencies asserting highly consequential power beyond what Congress could reasonably be understood to have granted.”

The court also ruled, on similar grounds, that the Centers for Disease Control and Prevention was not authorized to impose a moratorium on evictions and that the Occupational Safety and Health Administration was not authorized to tell large employers to have their workers vaccinated against Covid-19 or undergo frequent testing.

The states challenging the debt forgiveness program rely heavily on the doctrine.

“This is a major questions case,” the states wrote in a Supreme Court brief. Forgiving almost a half-trillion dollars owed to the Education Department, they added, is “undoubtedly a matter of economic and political significance.”

The administration, for its part, wrote in its brief that the major questions doctrine “does not justify overriding ordinary principles of statutory construction whenever an agency action can be described as consequential; rather, this court has applied the doctrine only in extraordinary cases characterized by what the court has concluded is a gross mismatch between an agency’s assertion of regulatory authority and the history and context of the supposed congressional authorization.”

In any event, the brief said, the plain text of the law that the administration relies on “supplies the clear authorization that the doctrine requires.”

The debt forgiveness program may have helped Democrats in November’s midterm elections. While voters as a whole split about evenly on the matter, with 50 percent supporting it and 47 percent opposing it, according to CNN exit polls, the program had far higher approval from younger voters, who broke decisively for Democrats.