By Stephen Dinan 

The Supreme Court has agreed to hear President Obama’s request to restore his deportation amnesty program, the justices announced in an order Tuesday that sets up the biggest showdown over executive powers in this administration.

The justices signaled they are interested in tackling the big questions of executive power, asking the lawyers for both sides to submit briefs on whether Mr. Obama’s amnesty violated the Constitution’s demand that the president “faithfully” execute the laws enacted by Congress.

Lower courts have held that Mr. Obama broke procedural and immigration laws in trying to grant work permits, Social Security numbers and three-year stays of deportation to more than 4 million illegal immigrants. But those courts shied away from reaching the major constitutional questions of presidential power.

The justices have sped the amnesty case along in order to hear it this term, meaning a ruling should come by the end of June. If Mr. Obama prevails, it would give him six months to begin implementing his policy, which he hopes will effectively lock it in for his successor.

Obama backers praised the court’s decision.

“The lives of millions of children and families in America have been disrupted and held in limbo – a situation the president’s action was designed to alleviate – and they deserve the Court’s careful and prompt attention,” said Elizabeth Wydra, chief counsel at the Constitutional Accountability Center.

Mr. Obama says he was only following what previous presidents have done, although on a grander scale, when he announced plans in November 2014 to grant “deferred action” to more than 4 million illegal immigrant parents and young adults who met certain conditions of age or family status.

Under deferred action, he said, he can grant illegal immigrants a three-year stay of deportation, which brings with it work permits, Social Security numbers and benefits such as access to tax credits.

Texas is leading 26 states in suing to stop the amnesty, arguing that it will have to grant driver’s licenses to hundreds of thousands of illegal immigrants, costing it money. Texas argues that Mr. Obama overstepped both his legal and constitutional boundaries, saying that the authors of the Constitution intended for Congress to decide big immigration policy debates.

Lower courts sides with Texas, saying while Mr. Obama has discretion to halt deportations, he cannot proactively grant them future stays of deportation, and other benefits, without going through the proper procedures or getting Congress to change the law.

Immigrant-rights groups say the deck was stacked against them both times, accusing District Judge Andrew S. Hanen of being “notoriously anti-immigrant,” and then saying the U.S. Fifth Circuit Court of Appeals was too conservative to give the case a fair hearing.

The case will test the conservative justices on the Supreme Court, who have grappled in the past over the deference they should show to executive power.

A ruling will come just weeks before both Republicans and Democrats nominate their presidential candidates at conventions in July, and whatever the justices decide will become a rallying point for both sides of the debate.

Mr. Obama said he felt forced to act after Congress failed to pass an immigration bill he wanted. Rather than issue an executive order, he had his Homeland Security secretary issue memos ordering agents and officers to stop deporting most illegal immigrants, and to expand an existing deferred action program to including millions of illegal immigrants.

He said he “took action to change the law” — a characterization that has landed him in hot water with several courts, who said that was evidence Mr. Obama was breaking the bounds put on him by the Constitution.