A bill that would make Missouri the latest state to adopt so-called right-to-work laws or policies passed the Republican-controlled House here on Thursday, but without enough votes to override an expected veto from the Democratic governor.

The business groups and conservatives that have for years pushed for a Missouri right-to-work law had hoped they would have enough votes this year to enact the measure, which failed last year. But Thursday’s vote, in which 23 Republicans joined Democrats in opposing the measure, suggested that the bill might again die this year.

Nevertheless, supporters of right-to-work laws, which allow workers who choose not to join a labor union to avoid paying the equivalent of dues, celebrated the bill’s passage even while they acknowledged that significant obstacles remained.

“Right-to-work will come to Missouri at some point in time — I think it’s inevitable,” said Representative John Diehl, a Republican and speaker of the Missouri House of Representatives. “Hopefully, we can get it done this year, but if not this year, it’s going to keep being an issue until it crosses the finish line.”

Even if the Senate, which is also controlled by Republicans, approves the bill, Gov. Jay Nixon said this week that he had never seen a right-to-work bill he would sign. Both chambers would have to muster two-thirds majorities to override a veto — but the House vote on Thursday, 91 to 64, fell well short of that margin.

One of the Republicans who voted against the bill was Representative Bart Korman, whose rural and suburban district west of St. Louis has a strong union presence. Mr. Korman said that his party colleagues were respectful of his position and that he did not foresee changing his mind if a similarly worded bill returned to the House for a vote to override.

Mr. Korman said unions had lobbied forcefully against a right-to-work law this year, as they had done in other states. Missouri is only the latest place in the Midwest to take up the issue. Six of the eight states that border Missouri have right-to-work policies, according to the National Right to Work Legal Defense Foundation. In neighboring Illinois, which does not have such a law or policy, the Republican governor issued an executive order this week that allows state employees there to opt out of paying union dues.

Mike Louis, president of the Missouri A.F.L.-C.I.O., said a right-to-work law would cause unions to lose members and, in turn, some of their negotiating power. He said he did not expect the right-to-work bill to become law this session.

“I think the workers who belong to the unions would suffer,” Mr. Louis said, “and that would bleed over to the middle-class workers who are not represented by unions.”

During hours of debate on the House floor this week, Republican after Republican spoke of job opportunities in Missouri that they claimed were lost to bordering states such as Kansas and Arkansas that have right-to-work laws or policies.

“States like Missouri with forced unionism are losing in population and revenue growth because unions don’t have to be responsive,” said Representative Eric Burlison, Republican of Springfield, who sponsored the measure.

Despite the bill’s failure to win a veto-proof majority, its passage underscored the commanding majorities Missouri Republicans have built in the Legislature in recent elections. Peverill Squire, a political-science professor at the University of Missouri, said those gains had given Republicans the ability to push a variety of laws, including a longstanding desire of some in the party to enact a right-to-work law.

Professor Squire said it was an open question whether the Senate would take up the measure this session. Even if senators approved it, he said, the governor’s veto threat means that enacting the measure would take an extraordinary effort.

“I think it’s a very slim chance,” he said.

Ed Martin, the chairman of the Missouri Republican Party, said he believed the legislative majorities were moving Missouri toward a right-to-work law. “I think we’re making progress,” said Mr. Martin, who noted that a right-to-work effort was not included in the state party’s official platform. “I just don’t know where the thing will stop this time.”