The Supreme Court gets down to work on Tuesday, hearing the first arguments of a new term.

Technically, the court term began on the traditional first Monday in October, but because it fell on the same day as the Jewish New Year, the court's three Jewish justices were absent and the remaining justices conducted only administrative business.

It's been eight months since Justice Antonin Scalia, a conservative icon, died unexpectedly. An hour after Scalia's death was confirmed, Senate Republican leader Mitch McConnell issued a statement declaring that there would be no hearings and no vote on anyone President Obama named to fill the vacancy. The seat, he declared, would be filled by the next president.

McConnell's been true to his word so far. Even after President Obama offered an apparent olive branch — nominating Merrick Garland, a centrist liberal judge long praised by Republicans — McConnell did not budge. Garland has now waited for a confirmation vote longer than any other Supreme Court nominee in history.

And the likelihood is that the seat will remain vacant for most of the current Supreme Court term as well. The only possibility for a nine-justice court prior to 2017 would be if Hillary Clinton is elected in November, and if McConnell were to allow a hearing and a vote during the lame-duck session of Congress prior to January. And that is something that, so far, the GOP Senate leader has pledged not to do.

That means that the court will remain short-handed, and often deadlocked, on some of the most controversial, and difficult, issues of the day.

Last term, the court deadlocked on a record four cases. A tie vote means the lower court decision prevails, for now, but sets no national precedent.

In the short term, that's not the end of the world, but as Justice Elena Kagan observed this summer, "a tie does nobody any good.

"We're there to resolve cases that need deciding, answer hotly contested issues," Kagan explained, "and you can't do that with a tie vote."

Kagan went on to praise Chief Justice John Roberts, who she said has "really tried to forge compromise" and "really tried to keep to a minimum the number of cases where we just throw up our hands and say we can't reach a decision."

But Kagan warned that, as the months tick by, the consequences grow more severe. Compromise is all well and good, she said, but last term some cases were decided on such narrow grounds that the court ultimately decided nothing of consequence, leaving unanswered the question the justices had initially planned to resolve, and leaving in place conflicting lower court decisions across the country.

"Over time that's a problem," said Kagan, "Is that cost free? No, it's absolutely not."

As the new term opens, there are already indications that Chief Justice Roberts is using every tool at his disposal to manage the situation. The court has accepted significantly fewer cases. And as to the most controversial cases accepted last year before Scalia died, several have not been scheduled for argument yet, as they normally would have been.

Perhaps the most contentious of these is a case that tests state constitutions that strictly forbid any direct or indirect aid to religious schools. Specifically, a church in Missouri is challenging the denial of a state grant to a church-run pre-school that wanted the money to rubberize the surface of its playground.

But as SCOTUSblog publisher Tom Goldstein observes, "when the big item on the agenda is what kind of rubber playgrounds we're gonna have at some churches, you know that so far it's a bit of a yawn."

That said, there are some important cases coming up.

One death penalty case could have a broad effect. In 2002, the Supreme Court ruled that states could not execute the "mentally retarded," but it didn't define what qualified as retardation, leaving that to the states. Now the issue is back, with death penalty opponents asking for stricter rules.

Then, too, there are cases that test when state legislatures can draw district lines that critics say minimize the impact of the black vote but defenders say minimize the impact of the Democratic vote. And headed back to the court are tests of strict voter ID laws enacted by Republican legislatures in 2013 after the Supreme Court, by a 5-4 vote, struck down a key provision of the Voting Rights Act.

Copyright 2016 NPR. To see more, visit http://www.npr.org/.