The Supreme Court's first day of oral arguments featured questioning by Justice Neil Gorsuch about the court's role in applying the immigration policies administered by the president.

The justices on Monday reheard arguments in Sessions v. Dimaya, a case the high court first heard before Gorsuch joined the court. The Supreme Court's decision to listen to arguments for a second time on the case about the deportation of non-citizens for committing crimes suggests the justices may be deadlocked and in need of Gorsuch's input.

At issue in Sessions v. Dimaya is the Department of Homeland Security's 2010 decision under the Obama administration to view the residential burglary convictions against James Garcia Dimaya as crimes of violence even though the burglaries did not involve violence. The Department of Homeland Security sought to deport Dimaya, a lawful permanent resident in the U.S. since 1992 and a citizen of the Philippines, and immigration judges agreed with DHS' decision.

The 9th Circuit Court of Appeals, however, thought the provision used to justify Dimaya's deportation proceedings was too vague, and the government's challenge arrived at the Supreme Court, with the Trump administration backing the Obama administration's decision.

Edwin Kneedler, deputy solicitor general, urged the justices to "pause greatly" before striking down the provision that he said is used all the time in immigration proceedings. Kneedler argued that such provisions are purposefully written in "very broad and general" terms, giving the president discretion.

Gorsuch interrupted Kneedler to note, "You're not asking the executive to define these crimes, you're asking us to."

Kneedler, representing the Trump administration, repeatedly sparred with Gorsuch about how to resolve the case.

"If I can't distinguish my job from a legislative body's work, am I infringing on a separation of powers problem?" Gorsuch asked.

Kneedler responded that such a problem might exist at the "margins" of the case and sought to avoid Gorsuch's questions about how the government thought the Supreme Court should define the disputed statute.

Joshua Rosenkranz, the lawyer representing Dimaya, appeared to tailor his arguments toward winning Gorsuch's vote.

"Justice Gorsuch is right — this is not a job the Congress can delegate to the courts and enforcement officials on the ground," Rosenkranz said at the beginning of his argument.

But Gorsuch pressed Rosenkranz, too, about the vagueness of the statute. After several repeated questions from Gorsuch about how to determine the "crime of violence" provision's application in civil cases versus criminal cases, Justice Sonia Sotomayor interrupted Rosenkranz to lend Gorsuch a helping hand.

"I get that you don't want to answer," Sotomayor said to Rosenkranz as Gorsuch laughed, but Sotomayor said she was interested in the answer, too.

If Gorsuch voted to support the 9th Circuit Court's ruling that the law is too vague, as Rosenkranz wishes, Gorsuch's vote could be decisive in resolving the case. Such a decision from Gorsuch may suggest he favors letting Congress and the executive branch develop immigration policy, unlike some of his Supreme Court colleagues who have taken a more hands-on approach.