The examples of Michigan and Indiana, where right-to-work laws took effect earlier this decade, suggest that the legislation could have cost unions thousands of members and millions in revenue.

One question is the extent to which the victory could reverberate beyond Missouri.

“I think this will build momentum and send a message to all legislators,” Mr. Trumka said, “that if you vote against the people, go against the will of the vast majority of working Americans, it’s going to cost you.”

But it was not immediately clear that the forces driving the impressive showing for labor in Missouri could be reproduced elsewhere.

One reason is that Republican voters who buck their party on a ballot measure, as many appeared to do in Missouri, may be unwilling to vote against Republican candidates in a general election, even when those candidates are hostile to labor.

“There’s a big difference between overturning the law itself and defeating legislators who supported it,” said Jonathon Prouty, a Missouri political consultant and former executive director of the state’s Republican Party. “It’s a lot easier for unions to energize their base around the issue, which is right to work, rather than against candidates.”

T. J. Berry, a Republican state representative whose district includes some outer suburbs of Kansas City, said that many of his constituents were proud union members who opposed right to work but nonetheless voted Republican because they were conservative on issues like abortion and guns.