The Supreme Court’s rejection on Friday of President Biden’s student debt relief plan instantly unravels one of the president’s signature efforts and ratchets up the pressure on him to find a new way to make good on a promise to a key constituency as the 2024 presidential campaign gets underway.

When Mr. Biden announced last summer that his government would forgive up to $20,000 in federal student loan debt, student advocacy groups and many progressives cheered the move, which was projected to help 40 million people and cost $400 billion.

“People can start finally to climb out from under that mountain of debt,” Mr. Biden said.

His plan, which came after months of agonizing about who it would benefit and whether it was too costly, would have been a centerpiece of his argument to voters that his economic agenda is designed to help low- and middle-income Americans blaze a path to greater prosperity.

Instead, a majority of the justices agreed with critics who said the president’s debt relief plan went beyond the president’s authority under congressional legislation allowing changes to student loans during a public emergency.

A White House official said Friday that Mr. Biden would soon denounce the court ruling and make it clear that he would continue to fight for debt relief. The official said that the president would “announce new actions to protect student loan borrowers.”

The official, who asked for anonymity to discuss strategy ahead of Mr. Biden’s remarks, said the White House would blame Republicans for being responsible for denying relief to those who have federal student loans.

That challenge for Mr. Biden and his advisers is exactly how to respond to the disappointment of millions of his supporters who again face the daunting prospect of paying back tens of thousands of dollars in debt they accumulated for college.

For much of the last year, administration officials have refused to say whether they were working on a “Plan B” in the event the Supreme Court rejected the president’s plan.

Even after several justices expressed deep skepticism during oral arguments earlier this year, Mr. Biden and his aides continued to insist that they had confidence in the legality of the debt relief plan and would not say whether they were working on an alternative.

In fact, advocates believe there are ways for the federal government to provide debt relief to some students even in the wake of the court’s ruling. The administration has already been offering help to some students using Public Service Loan Forgiveness, a program which provides debt relief to people who work full time for state, local, federal or non-profit organizations.

The administration has already said it will make more use of existing programs that allow lower-income people to adjust their repayment plans based on their income.

But the existing debt relief programs are more targeted and affect a far smaller population of people. They are not likely to satisfy the frustrations of tens of millions of people who had expected their financial situation to improve dramatically under Mr. Biden’s plan.

And millions of people with federal student loans are about to get another financial shock this fall, when the years long pause on repayment of existing loans ends.

The federal government, under former President Donald J. Trump, imposed the pause on repayments at the beginning of the pandemic, as businesses shut their doors and millions of people lost their jobs. Mr. Biden renewed the pause several times since taking office, but has said it will not be renewed again now that the pandemic has largely ended.

Payments are set to resume in October, putting new pressure on the very debt-holders that Mr. Biden’s forgiveness plan was designed to help.

One question for Mr. Biden is whether those who are disappointed will blame him or the Supreme Court when the go to the ballot box next year.

During his 2020 campaign, Mr. Biden vowed to eliminate some student debt, saying during a town hall even that “I’m going to make sure that everybody in this generation gets $10,000 knocked off of their student debt as we try to get out of this God awful pandemic.”

Once in office, many Democrats — including Senator Chuck Schumer of New York, the top congressional Democrat — implored Mr. Biden to go even further, urging the president to wipe away as much as $50,000 per person in student debt as a way of helping middle-income people who are struggling financially.

After Mr. Biden announced his plan last summer, student activists said the plan would energize young people to support the president. That support could be in doubt in the wake of the Supreme Court’s ruling.