The justices on Tuesday took no action on the administration's request that it review the Deferred Action for Childhood Arrivals program, which has protected nearly 700,000 people brought to this country as children, commonly known as "dreamers."
If the court sticks to its normal procedures, that would mean that even if it accepts the case as a later date, it would not be argued until the new term starting in October, with a decision likely in 2020.
DACA has emerged as an issue in the negotiations over ending the partial government shutdown, with President Donald Trump offering extended but still temporary protection for those in the program in exchange for billions of dollars to build a border wall. Democrats have rejected the offer as "hostage-taking."
Trump has previously said he wanted the Supreme Court to take the case and find he had the authority to end the program.
A string of lower of lower courts have said that Trump's abrupt decision to terminate the Obama-era program was based on faulty legal reasoning and that the administration has failed to provide a solid rationale for ending it.
The Trump administration moved to scuttle the program in 2017 after Texas and other states threatened to sue to force itsend. Then-Attorney General Jeff Sessions advised the Department of Homeland Security that the program was probably unlawful and that it could not be defended.
But courts have rejected that theory and kept the program in place, requiring that those already enrolled be allowed to renew their participation. California Attorney General Xavier Becerra, who is among those fighting the administration's decision to end the program, said more than 276,000 two-year renewals have been approved in the past year.
Those approved to be in the program are allowed work permits and protected from deportation, as long as they abide by its regulations and do not violate laws.
The judges who have stopped the termination of the program have said the administration could remedy the legal impasse by providing a detailed reasoning of why the program should end. Instead, it has continued to combat the orders in court.
The fight over the young people protected by the program - the average age of those in the program is around 24 - has been a fierce battle between Trump and Democrats, who largely defend the initiative program.
Trump at times has said he would like to find a way to protect those in the program, but attempts to work out a political compromise over DACA have foundered amid the larger partisan debate over immigration and border security.
Solicitor General Noel Francisco, representing the administration at the Supreme Court, said in a brief that the cases "concern the Executive Branch's authority to revoke a discretionary policy of non-enforcement that is sanctioning an ongoing violation of federal immigration law by nearly 700,000 aliens."
While the Supreme Court has never considered the legality of DACA, it did hear a challenge to an Obama program to extend deportation protection to undocumented parents of those who are either American citizens or lawful permanent residents. Operating with only eight justices because of the death of Justice Antonin Scalia, the court split 4 to 4 - thus leaving in place a lower court decision that stopped the program.
Francisco said DACA is "materially indistinguishable" from that program and that courts would likely find it illegal.
But so far, federal courts in California, New York and the District of Columbia have said that reasoning is wrong. (A judge in Texas said the program was illegal, but did not rule it should cease.) The judges who have ruled against the Department of Homeland Security's justification for ending DACA say it must be based on more than just a belief about its legal underpinnings.
A panel of the U.S. Court of Appeals for the 9th Circuit last month ruled against the administration.
"To be clear: we do not hold that DACA could not be rescinded as an exercise of Executive Branch discretion," Judge Kim McLane Wardlaw said in the opinion. "We hold only that here, where the Executive did not make a discretionary choice to end DACA - but rather acted based on an erroneous view of what the law required - the rescission was arbitrary and capricious under settled law."
The judges, all nominated by Democratic presidents, flatly rejected the administration's position that courts lacked the power to review the executive branch's immigration actions.
"The government may not simultaneously both assert that its actions are legally compelled, based on its interpretation of the law, and avoid review of that assertion by the judicial branch, whose 'province and duty' it is 'to say what the law is,' " Wardlaw said, borrowing the language of the landmark Marbury v. Madison decision.
The regents of the University of California, one of the parties challenging the administration, told the Supreme Court there was no hurry to take the case because each DACA recipient had been vetted by the federal government.
The university leadership quoted a tweet from Trump to argue that not even this administration was advocating immediate deportation of those in the program.
"Does anybody really want to throw out good, educated and accomplished young people who have jobs, some serving in the military? Really!" the president tweeted in September.
The case is Department of Homeland Security v. Regents of the University of California.