Chief Justice John Roberts and Justice Anthony Kennedy, two key votes on the nine-member court, indicated during an 80-minute oral argument in the case involving California teachers that they could side with the three other conservative justices in delivering a ruling overturning a 1977 high court precedent.

U.S. conservatives have long sought to curb the influence of unions representing public employees like police, firefighters and teachers that often support the Democratic Party and liberal causes. The case before the justices was spearheaded by a conservative group called the Center for Individual Rights.

A ruling in favor of the non-union teachers would be a blow to organized labor because unionized teachers and other civil servants in states without “right-to-work” laws comprise its main power base. Public sector workers are almost six times more likely to belong to a union than those in the private sector.

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