"I do think this is a very sad day in Michigan history," Constance said.
The crowds filled the rotunda area, beating drums and chanting. The chorus rose to a deafening thunder as House members voted. Later, protesters surged toward a building across the street housing Snyder's office. Two people were arrested when they tried to get inside, state police said.
By late afternoon, the demonstrators had mostly dispersed.
The governor insisted the matter wasn't handled with undue haste, calling the debate in the House and Senate a "healthy discussion."
Michigan gives the right-to-work movement its strongest foothold yet in the Rust Belt, where the 2010 election and tea party movement produced assertive Republican majorities that have dealt unions repeated setbacks.
Opponents said they would press Snyder to use his line-item veto authority to remove a $1 million appropriation from the bills, making them eligible for a statewide referendum. But the House swiftly rejected a Democratic amendment to that effect.
Lawmakers who backed the bills "will be held accountable at the ballot box in 2014," said state Rep. Tim Greimel, the incoming House Democratic leader.
But Sen. John Proos, a Republican from St. Joseph who voted for both bills, predicted that objections would fade as the shift in policy brings more jobs to Michigan.
"As they say in sports," he said, "the atmosphere in the locker room gets a lot better when the team's winning."
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