Republicans have one last shot to pass health-care legislation while they’re in control of both chambers of Congress and the presidency—and industry lobbyists expect them to use the opportunity to bite off smaller bills that can be bundled together or tacked onto larger legislation.

The Pharmaceutical Research and Manufacturers of America has been pushing Congress to reduce drugmakers’ contributions to close the Medicare Part D coverage gap, known as the doughnut hole, by $4 billion. PhRMA, as the group is...