LANSING, Mich. — With Democratic furor escalating and party leaders warning that Michigan was about to be plunged into lasting political discord, the state’s Republican-led Legislature was on the verge of approving new limits to unions here in the birthplace of the modern labor movement.

Republicans said they intended to cast final votes as early as Tuesday on legislation abruptly announced last week that would bar workers from being required to pay union fees as a condition of employment, even as thousands of union members planned to protest at the state Capitol and as President Obama, visiting a truck factory outside Detroit, denounced the notion.

“You know, these so-called right-to-work laws, they don’t have to do with economics,” Mr. Obama said. “They have everything to do with politics. What they’re really talking about is giving you the right to work for less money.”

From a distance, there would seem no more unlikely a target for this fight than Michigan, where labor, hoping to demonstrate strength after a series of setbacks, asked voters last month to enshrine collective bargaining into the state Constitution.