Lesa Curtis of Westchester, N.Y., right, who is in favor of agency fees and a former president of her union, rallies outside the Supreme Court on Monday as the court hears arguments in the Friedrichs v. California Teachers Association case. (Jacquelyn Martin/AP)

A majority of the Supreme Court on Monday seemed prepared to hand a significant defeat to organized labor and side with a group of California teachers who claim their free speech rights are violated when they are forced to pay dues to the state’s teachers union.

By their questioning at oral argument, the court’s conservatives appeared ready to junk a decades-old precedent that allows unions to collect an “agency fee” from nonmembers to support collective-bargaining activities for members and nonmembers alike.

It is the most important Supreme Court case of the year for unions and one of a clutch of politically charged cases that puts the justices in the spotlight as the nation turns its attention to the elections of 2016.

[Justices agree to hear dispute over union fees, reapportionment]

The case involves only public-employee unions — not private workers — but those unions are the strongest segment of an organized labor movement that is increasingly tied to the Democratic Party. At the same time, Republican governors across the nation have become embroiled in high-profile battles with the public-employee unions in their states.

Conservative groups have directly asked the court to overturn a 1977 decision, Abood v. Detroit Board of Education, that favored the unions. That ruling said that states could allow public-employee unions to collect fees from nonmembers to cover the costs of workplace negotiations but not to cover the union’s political activities.

The unions say losing those fees would be a heavy blow because there is no incentive for workers to pay for collective-bargaining representation they could receive for free. About 20 states, including California, allow what the unions like to call “fair-share” fees.

But conservative justices sharply questioned whether it was possible to separate public-employee negotiations from the kind of public policy questions — teacher salaries and classroom sizes, for instance, and the tax dollars that must be raised to pay for them — that are raised.

“When you are dealing with a governmental agency, many critical points are matters of public concern,” said Justice Anthony M. Kennedy, who traditionally is the most likely of the court’s conservatives to join with liberals to form a majority.

Some teachers disagree with their unions on issues such as merit pay, promotion and the importance of seniority, Kennedy said.

[Two teachers explain why they want to take down their union]

The fees “require that employees and teachers who disagree with those positions must nevertheless subsidize the union on those very points,” he said.

It is not enough to argue that the teachers can speak out on their own as citizens, he said.

In the current case, union leaders were not counting on Kennedy but on another conservative, Justice Antonin Scalia.

Scalia in the past has expressed sympathy for the view that the unions needed to collect the fees to prevent “free riders” — those who benefit from the agreements that unions reach with government employers but who do not pay for the union’s costs. But he did not pose any questions Monday that favored the union’s view and said he shared Kennedy’s concerns.

“The problem is that everything that is collectively bargained with the government is within the political sphere, almost by definition,” he said.

He also questioned the contention that the unions would not survive without collecting the fees. Already, there are 25 states that do not require their collection, and Scalia said the unions should do a better job of persuading those eligible to join.

California Solicitor General Edward C. DuMont, who was aligned in the case with the teachers union, said the California unions already had extraordinary participation but prohibiting agency fees fights human nature.

“Many people can want something in the sense they view it as very advantageous to themselves, but if they are given a choice, they would prefer to have it for free, rather than to pay for it,” he said. “This is a classic collective-action problem.”

Oral arguments are not always predictive, but it seemed clear that DuMont, California Teachers Association attorney David C. Frederick and Solicitor General Donald B. Verrilli Jr., representing the Obama administration, were treading against the tide.

The court’s five conservatives in 2012 and 2014 had expressed grave doubts about whether the Abood decision had properly taken into account the First Amendment rights of the union objectors.

It has been the pattern of the court headed by Chief Justice John G. Roberts Jr. to take incremental steps toward undermining a precedent with which it disagrees before delivering a final blow.

The court’s liberals said the challengers had not made the case for why the court should abandon a precedent rather than take the normal path of upholding it.

[Two teachers explain why they want to take down their union]

Justice Stephen G. Breyer said the Abood “compromise” had worked pretty well over the last 40 years. When the court starts overruling precedents, he said, “What happens to the country thinking of us as a kind of stability in ­­a world that is tough because it changes a lot?” Breyer asked.

Justice Elena Kagan also pushed that theme, telling Washington attorney Michael A. Carvin, who represented the objecting teachers, that he had a “heavy burden.”

“That’s always true in cases where somebody asks us to overrule a decision. It seems to be particularly true here,” Kagan said. “This is a case in which there are tens of thousands of contracts with these provisions. Those contracts affect millions of employees, maybe as high as 10 million employees. So what special justification are you offering here?”

Carvin replied that the strongest reason for overturning a precedent is when it “erroneously denies a fundamental right’’ — in this case, freedom of speech and association.

Kagan and other justices said the court’s precedents were clear that when government is acting as an employer, it can act as any employer in restricting employee rights.

Frederick argued for leaving the decision about requiring fees to the individual states, rather than forbidding the process. “Different states have different experiences, and this is an opportunity for the states to draw upon those distinctive experiences in coming up with a system that’s fair for everyone,” he argued.

There seemed to be two options if a majority disagreed with Abood but was reluctant to overturn the precedent.

The justices could remand the case to the lower courts. Carvin and his clients had raced through the lower courts in hopes of getting the case to the Supreme Court faster.

The justices could also change how the agency fees are collected. Currently, the fees must be paid, and then employees “opt out” of funding the union’s political activities and receive money back. Objecting employees say that minimizes the burden on them.

But there was limited questioning from the justices about whether such a change might be an alternative to overturning the system.

The case is Friedrichs v. California Teachers Association.