BOSTON -- Labor leaders are urging lawmakers to move quickly to override Gov. Charlie Baker's veto of a proposal giving unions more access to public sector workers.

The legislation, which was aimed to soften the blow of a U.S. Supreme Court ruling, would allow unions representing public workers to charge non-members for the cost of representing them in the grievance process. It would also give labor officials access to new hires and non-union members in state and local government to talk with them about joining a union.

It was handily approved by the Democratic-controlled House and Senate in June with support from the Legislature's Republican minority, but Baker returned the bill to lawmakers with proposed amendments, including prohibiting the disclosure of workers' cellphone numbers and personal information, and not requiring them to meet with labor representatives.

Lawmakers, however, ignored the proposed changes and sent the bill back to the governor for consideration.

On Friday, Baker returned the bill again, this time unsigned -- a move known as a "pocket veto" -- saying provisions of the legislation still violate employees' privacy rights.

In a letter to lawmakers, Baker reiterated that he supports workers' rights to join a public sector union but won't sign legislation "that compels state and municipal government to turn over the cell phone numbers of private citizens, who happen to be government employees, without their permission, to private organizations."

Union leaders say the protections are necessary and that cell phone numbers are the best way to reach government workers to inform them about the benefits of membership.

"Unions aren't looking to harass government workers at home or work," said Jim Durkin, a spokesman for the American Federation of State, County and Municipal Employees Council 93, which represents about 45,000 public sector employees in Massachusetts and three other states. "We simply want to be able to reach out to them to let them know about their rights."

The proposal was filed in response to last year's U.S. Supreme Court ruling, which held that government workers cannot be forced to contribute to labor unions.

In its ruling, the court sided with Mark Janus, an Illinois child support specialist who does not belong to the union and fought its $45 monthly fee for covering him in contract negotiations. He argued that his money helped finance the union’s political activities, thus violating his free speech rights.

The decision ended a provision in Massachusetts and 21 other states requiring public workers to pay "fair share" fees to unions as a condition of employment, even if they don’t want to be members. The fees are meant to offset unions' costs of collective bargaining and contract administration that benefit all employees.

Union leaders say the protections are needed to safeguard workers' rights and push back against conservative groups seeking to reduce public sector membership. They say workers who enjoy union benefits, such as legal representation in arbitration hearings, should have to pay something.

Conservative groups say Democrats, and the labor unions that heavily fund their campaigns, are trying to find a way around the court ruling to drum up dues. Organized labor spends millions of dollars lobbying Beacon Hill through political action committees, and most of the money goes to Democrats, according to the Pioneer Institute.

Paul Craney, a spokesman for the Massachusetts Fiscal Alliance, praised Baker's decision to veto the bill and urged lawmakers to reconsider an override.

"Legislative leaders should get the message, the Janus 'fix' needs to be fixed," he said in a statement. "It went too far and only benefited union bosses at the expense of workers."

Christian M. Wade covers the Massachusetts Statehouse for North of Boston Media Group’s newspapers and websites. Email him at cwade@cnhi.com.