Voters in four states will decide Nov. 6 whether to expand Medicaid under the Affordable Care Act, with the initiatives spurring some $20 million in political spending and testing the public’s appetite for expansions in states where the ACA remains unpopular.

Top spenders in the campaigns are groups linked to the tobacco industry and the Koch brothers, which are aligned against the initiatives, and hospitals and union-back advocacy groups, which are in favor of them.

Residents...