WASHINGTON — Justice Antonin Scalia’s death deprives conservatives of a key vote that could change the outcome in some major Supreme Court cases, including one in which labor unions appeared headed for a big defeat.

Next month’s Supreme Court arguments over contraceptives, religious liberty, and President Obama’s health care law also now seem more likely to favor the Obama administration.

Those are the most immediate effects on the court of the loss of its conservative icon and longest-serving justice.

It’s a firm Supreme Court rule that decisions are not final until they are handed down. So nothing Scalia did or said in pending cases matters to the outcome.

‘‘The vote of a deceased justice does not count,’’ veteran Supreme Court lawyer Roy Englert said Sunday, a day after Scalia was found dead in his room at a West Texas ranch.

Subtracting Scalia’s vote from cases in which he was in the majority in a 5-to-4 split leaves the result tied.

The remaining eight justices have two options in that situation: They can vote to hear the case a second time when a new colleague joins them or they can hand down a one-sentence opinion that upholds the result reached in the lower court without setting a nationwide rule.

A second round of arguments seems less likely at the moment because a new justice may not be confirmed until the next president is in office.

A tie vote, by contrast, resolves the case at hand and allows the legal issue to return to the court at a later date when there is a ninth justice.

Public sector labor unions had been bracing for a stinging defeat in a lawsuit over whether they can collect fees from government workers who choose not to join the union. The case affects more than 5 million workers in 23 states and the District of Columbia and seeks to overturn a nearly 40-year-old Supreme Court decision.

Now, what seemed like a certain 5-to-4 split, with the conservatives in the majority and the liberals in dissent, instead looks like a tie that would be resolved in favor of the unions, because they won in the lower courts.

‘‘That’s a big loss. It was all teed up and it looks like it’s not going to go anywhere now,’’ said Brian Fitzpatrick, a Vanderbilt University law professor who had served as a clerk to Scalia.

Another case in which there now seems little chance of finding a court majority to upset long-standing practice involves a conservative challenge to the way governments have drawn electoral districts for 50 years.

The court heard arguments in December in a case from Texas on the meaning of the principle of ‘‘one person, one vote,’’ which the court has said requires that political districts be roughly equal in population.

But it has left open the question of whether states must count all residents, including noncitizens and children, or only eligible voters in drawing district lines.