Of the remaining cases argued during the court's current term, which began in October, the most eagerly awaited one concerns a Missouri church backed by a conservative Christian legal group. The ruling potentially could narrow the separation of church and state.
A decision in favor of Trinity Lutheran Church, located in Columbia, Missouri, set the stage for more public money to go to religious entities. The church sued after being denied state taxpayer funds for a playground improvement project because of a Missouri constitutional provision barring state funding for religious entities.
Trinity Lutheran could be headed for a lopsided win, with two liberal justices joining their conservative colleagues in signaling support during the April oral argument. It was one of the first in which Trump's conservative appointee to the court, Neil Gorsuch, participated.
The dispute pits two provisions of the U.S. Constitution's First Amendment against each other: the guarantee of the free exercise of religion and the Establishment Clause requiring the separation of church and state.
A broad ruling backing the church could hearten religious conservatives who favor weakening the wall between church and state, including using taxpayer money to pay for children to attend private religious schools rather than public schools. President Donald Trump's education secretary, Betsy DeVos, is a leading supporter of such "school choice" plans.
The most notable of three immigration-related cases in which rulings are due on Monday is a dispute over whether immigrants detained by the U.S. government for more than six months while deportation proceedings unfold should be able to request their release. The case takes on additional significance with Trump ratcheting up immigration enforcement, placing more people in detention awaiting deportation.
The court also is set to decide a case that could clarify the criminal acts for which legal immigrants may be deported. Another involves whether the family of a Mexican teenager shot dead while standing on Mexican soil by a U.S. Border Patrol agent in Texas can sue for civil rights violations.
As the justices look to finish work before their summer break, they must decide what to do with Trump's travel ban, which was blocked by lower courts. His administration has made an emergency request asking for the ban to go into effect while the litigation continues.
The March 6 executive order called for a 90-day ban on travelers from Libya, Iran, Somalia, Sudan, Syria and Yemen and a 120-day ban on all refugees entering the United States to let the government implement stronger vetting. Trump has said the order is needed urgently to prevent terrorism in the United States.
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