The new date is Jul 21, 2022.
The high court will hear the case later this year, marking the latest Biden immigration policy to get caught in the court system.
The high court declined to halt a lower court ruling from last month suspending ICE's enforcement guidelines, which told agents to prioritize arresting immigrants who threaten public safety or enter the U.S.
Four of the Supreme Court's nine members dissented from Thursday's decision.
The court will hear arguments in the case in December.
The Biden Administration asked the Supreme Court to stay the decision of the Texas judge who threw out the guidelines.
The Department of Homeland Security wouldn't say anything about the decision.
The Secretary of Homeland Security, Alejandro Mayorkas, argued that federal agents shouldn't arrest immigrants who contribute to their communities and pose no threat to the public. The policy was part of a series of actions taken by President Joe Biden to wind down some of the hardline immigration measures introduced by the Trump Administration. In the Biden era, ICE has pledged to avoid raiding worksites and deporting victims of crime, and border agencies have sought to wind down the policies of the Trump administration. Legal challenges from Republican states have been faced by this tactic. After Texas sued the administration within days of Biden's swearing in, Tipton tried to block an interim version of ICE's guidelines. Hundreds of thousands of migrants were quickly deported back to Mexico under Biden's Title 42 policy, which was stopped by a judge in May.
Last month, the Supreme Court ruled in Biden's favor on one immigration challenge, in which a lower court judge had ruled that the administration couldn't reverse a policy that required asylum-seekers to wait in Mexico for their day in immigration court.
There has been a spike in the number of people arrested at the U.S.- Mexico border. Border Patrol agents arrested a record-high 1.66 million people who tried to cross the border in the fiscal year that ended last September. Title 42 caused more people to try to cross the border multiple times.