A Federal Communications Commission plan to alter a phone and internet subsidy program is drawing fire from an odd-bedfellows coalition of telecom carriers, state officials and public interest groups.

CTIA, the wireless industry’s trade group, the National Association of Regulatory Utility Commissioners, and public interest groups are pressuring the commission to delay upcoming changes its Lifeline program, which serves low-income subscribers.

The array of opponents are often on different sides of communications policy fights, such as the one over net neutrality. But they agree that the FCC’s plan to alter Lifeline—which the Obama-era agency set in motion—would hurt consumers and...