New Justice Neil Gorsuch is set to make a major impact on the Supreme Court in his first week of oral arguments, which includes a major religious liberty case that conservatives hope swings their direction now that the appeals court judge has been added to the bench.

For the first time in more than a year, the Supreme Court will hear oral arguments this week with the full complement of nine justices. Oral arguments in Trinity Lutheran Church of Columbia v. Comer will be held Wednesday, when the high court will seek to decide whether Missouri violated the Constitution in its decision to bar a church from a state program that gives nonprofits funding to resurface their playgrounds. Missouri's Constitution includes a provision that prevents public funds from directly or indirectly assisting any church, sect or religion.

The high court's ruling in the Trinity Lutheran case could have a widespread impact on the three dozen other states with similar provisions in their state constitutions, and the decision could be narrowly decided.

The Supreme Court agreed to hear the case before Justice Antonin Scalia died, but the justices waited to hear oral arguments for several months, which allowed nine justices to again be seated on the bench.

"The court never gave any explanation for why it delayed scheduling the oral argument, but the natural inference is that scheduling was delayed because the court felt that it needed a ninth justice to decide this case," said Aaron Streett, chairman of Baker Botts' Supreme Court and Constitutional Law Practice, in a phone call with reporters. "Now I don't think they would have taken an internal vote, a preliminary vote, that sort of thing is not done until all the merits briefs are in and the oral argument is heard, but it does suggest that the chief justice who would take the lead on scheduling cases had at least some concern that this could end in a 4-to-4 decision such that it would be helpful to have a ninth justice in place."

Streett, who filed an amicus brief in the case on behalf of conservative lawmakers, said he thought Gorsuch's record as a 10th Circuit Court of Appeals judge would show him likely to align with Justices Clarence Thomas and Samuel Alito, as well as his predecessor, Scalia. But Streett cautioned against viewing the case as a "slam dunk" and thinks Gorsuch will grapple with the difficulties of the case just as much as the other justices.

Judicial Crisis Network chief counsel Carrie Severino said she thought Gorsuch would be unlikely to rule any differently from Scalia. However, she said she thought Gorsuch's presence on the court could have a "serious impact" on how it decides the case.

"I think this is a case where, and we'll know a little more during oral arguments, where it seems like you ought to be able to get some liberal votes," Severino said. "However, if [Gorsuch] weren't in the court and this did break down 4-4, then this is the kind of case where you could have had an evenly split court and Justice Gorsuch would be a key deciding vote in that case."

Liberals are concerned about how Gorsuch may affect the decision in the Trinity Lutheran case and similar controversies. Caroline Fredrickson, American Constitution Society president, said Gorsuch may be more "solicitous" of religious people's concerns than Scalia.

"[Gorsuch's] record shows that he is extraordinarily solicitous to those who express a religious belief to the detriment of others whose rights have been affected," Fredrickson said. "So I think there's certainly a great deal of concern about his pushing the court in that direction even further."

Severino said she thought the case should be open-and-shut, but Justice Anthony Kennedy could serve as a swing vote. Kennedy often serves in a fence-sitting capacity on contentious issues, and many conservatives hope that Gorsuch's status as a former Kennedy clerk means he can woo him to the right. Kennedy swore in Gorsuch at the White House last week.