WASHINGTON -- The Supreme Court opened a new term Monday and within weeks is set to hear cases on health care and religion that may give a preview of how the conservative majority will wield its power.

But the eight justices also face a month of unusual uncertainty. They will wait to see if a new justice is confirmed, whether President Donald Trump is reelected in early November and whether they are called upon to decide any disputes that arise if the election is very close.

The outcome of the election will surely shape the term ahead, even though many of the cases are already set. The justices will find themselves weighing cases on immigration, the census and health care from a triumphant conservative administration, or a series of last-gasp appeals from a defeated president.

Either way, the term's initial cases will be heard by a court with a conservative majority -- 6-3 if Trump's choice, Amy Coney Barrett, has won confirmation or 5-3 if her nomination has stalled. The defining issue of the year seems likely to be how aggressively that conservative majority will move.

An early test is set to come a week after the election when the justices take up the latest challenge to President Barack Obama's Affordable Care Act.

Despite his promises, Trump failed to "repeal and replace" the health care law when Republicans controlled Congress. Now, he and his lawyers are pressing the high court to strike it down amid the COVID-19 pandemic. They contend that when the tax penalty for not having insurance was reduced to zero in 2017, it had the effect of cutting out the pillar that propped up the far-reaching law.

"The entire ACA thus must fall with the individual mandate," Trump's lawyers told the court.

If the court's conservatives were to agree, it would cancel the insurance subsidies for nearly 30 million Americans as well as the insurance protections for more than 50 million others who could be denied coverage because they have a preexisting medical condition. The law also made health care screenings at no cost for children and adults a standard part of a medical checkup.

The case is called California vs. Texas because California Attorney General Xavier Becerra and a coalition of Democratic-led states stepped in to the defend the law after the administration joined with Texas and a group of Republican states that sued to kill it.

"A preexisting medical condition should never again disqualify you from receiving affordable health care," Becerra said in response to the administration's appeal.

The oral argument is set for Nov. 10. The nation should know by then whether Trump has been reelected or defeated.

Prior to the death of Justice Ruth Bader Ginsburg, this latest challenge to the health care law looked headed for defeat. Five members of the court -- including Ginsburg and Chief Justice John G. Roberts Jr. -- rejected legal attacks on the law in 2012 and 2015.

They did so in the face of fierce dissents from four conservatives who said the entire law should be voided. They were Justices Antonin Scalia, Anthony Kennedy, Clarence Thomas and Samuel A. Alito Jr.

Thomas and Alito remain on the court, and they will be joined by Trump's appointees -- Justices Neil M. Gorsuch, Brett M. Kavanaugh and, quite likely, Barrett -- who see themselves as proteges of Scalia or Kennedy.

Nonetheless, most legal experts, including critics of the law, see this latest challenge as a weak one and predict that even a more conservative court will reject it.

There are two questions before the justices: Is the so-called individual mandate -- the requirement that people purchase health insurance -- unconstitutional now because there is no longer any penalty to enforce it? And if so, must the rest of the law be declared unconstitutional as well?

Lawyers for Texas convinced a federal judge in Fort Worth that the mandate is now unconstitutional and that the entire law must be voided. The Supreme Court, however, has taken a much more cautious approach to striking down sweeping measures even if one provision is found to be invalid. Instead, they invoke what is called the "severability doctrine."

In early July, Kavanaugh wrote an opinion for the court that is sure to be quoted in the health care case. By a 7-2 vote, the court upheld a 1991 federal law banning robocalls, despite finding one provision unconstitutional. Kavanaugh wrote that there is a "strong presumption" against voiding laws because of one defect. Instead, the flawed provision may be severed or removed, while the rest is preserved.

"Constitutional litigation is not a game of gotcha against Congress, where litigants can ride a discrete constitutional flaw in a statute to take down the whole, otherwise constitutional statute," Kavanaugh said.

Only two justices -- Thomas and Gorsuch -- disagreed.

Another early opportunity for the conservatives will come the day after the election, when the justices will hear a claim from conservative Christians who say they have a religious right to be exempted from anti-discrimination laws that protect LGBTQ people.

Two years ago, the court ruled in favor of a Colorado baker who refused to make a wedding cake for a same-sex couple, but it did so without setting a legal rule. Instead, the justices said only that a state civil rights commission had impermissibly displayed "hostility" toward the baker.

In the new case, Catholic Social Services sued the city of Philadelphia after it lost its annual contract for caring for foster children and placing them with foster parents. The city acted after learning that, unlike more than two dozen other private foster agencies, the Catholic agency had said it would not place children with same-sex couples.

Foster placements with same-sex couples would violate the church's teaching that marriage is limited to a man and a woman, its officials said.

Lawyers for the agency say that excluding them violated the church's First Amendment right to the "free exercise" of religion and the freedom of speech.

Philadelphia, by contrast, says its ordinances forbid contractors from discriminating based on race, religion, national origin or sexual orientation.

A federal district judge and the 3rd Circuit Court ruled for the city. The appeals court said the "city's nondiscrimination policy is a neutral, generally applicable law, and the religious views of CSS do not entitle it to an exception from that policy." The lower courts cited a 1990 opinion written by Scalia.

Back when Scalia wrote that decision, conservative justices were skeptical of courts giving religious claimants special exemptions from laws that apply to everyone. More recently, however, the court's conservatives have signaled a change of mind and suggested they may overrule Scalia's opinion.

The new case -- Fulton vs. Philadelphia -- will come before a court with five conservative justices who were raised as Catholics -- six if Barrett is confirmed. One other Catholic justice, Sonia Sotomayor, is a member of the court's liberal minority.

The justices are also due to act soon on an emergency appeal from the Trump administration regarding whether to make it easier or harder for pregnant women to obtain abortion pills during the pandemic.

Current rules require women to travel in person to a clinic or hospital to pick up the medication rather than have it delivered through the mail. A federal judge in Maryland, agreeing with national medical groups, said this rule made little sense during the pandemic when a patient was interacting with her doctor through telemedicine rather than in person. The trip could also expose her to a risk of contracting the virus.

The judge ordered the rule temporarily suspended. But in early September, Trump's lawyers asked the Supreme Court to intervene and restore the rule. They argued a judge had no authority to waive such a medical rule.

Usually the justices act on such emergency appeals within a week or two, but this one has not been resolved. Ginsburg's death on Sept. 18 may have stalled a decision. Now the eight justices must decide whether to make their first ruling since Ginsburg's death on an issue involving women and abortion.