As Republican leaders in Washington grappled after the election with their failure to unseat President Obama, Dick DeVos, one of Michigan’s wealthiest men, began dialing up state lawmakers in Lansing.

Although Mr. Obama won Michigan handily, Republicans had kept control of the Legislature. A union-backed ballot measure to enshrine collective bargaining rights in the State Constitution was defeated, thanks to an aggressive campaign against it that was financed in part by $2 million of DeVos family money.

The time had come, Mr. DeVos told Republican lawmakers, for the bold stroke they were considering: a law banning requirements that workers pay union dues or fees, in the state where the modern American labor movement was born. If the lawmakers later found themselves facing recalls or tough re-election fights, Mr. DeVos told them, he would be there to help.

“That was when I started to say, you know what, this thing could happen,” Mr. DeVos said on Friday. “These people really are serious and committed.”