The Nebraska measure takes the minimum hourly wage to $9 by 2016, while Arkansas goes to $8.50 by 2017. South Dakota's new initiative will raise the bar to $8.50 by 2015, and the nonbinding Illinois measure calls for a $10 minimum wage by 2015. President Barack Obama has called for raising the federal minimum raise to $10.10 an hour from the current $7.25.
The Alaska measure will boost the minimum wage to $8.75 from $7.75 beginning in 2015, with an additional dollar raise the next year.
The Arkansas, Nebraska and Alaska initiatives all passed easily, garnering more than 60 percent of the vote.
Read MoreIn states voting on wage, even opponents sound like supporters
"The polling on minimum wage is very clear: It is something that three-quarters of the country supports," said Michael Strain, a resident scholar at the conservative American Enterprise Institute who specializes in labor market and federal budget policy.
That apparent national majority has also affected the rhetoric of many Republicans, experts told CNBC. In fact, some suggested that a new federal agreement on the matter may be in store for the GOP-led Senate if it could be adequately tied to tax reform.
And while Strain said Republicans may well want to avoid the subject if they can help it, other analysts said the party will have to address the issue to gain credibility by showing investors and businesses that it can compromise.
"Something is changing: Traditionally one might think that a Republican regime would not be supportive of raising wages, but that classical model may be falling apart," said Richard Hastings, macro strategist at Global Hunter Securities.
Although a grand bargain involving wages and taxes proved elusive during the Democrats' control of the Senate, Hastings said he is watching for congressional changes from Tuesday's midterm results.
—CNBC's Ben Berkowitz contributed to this report.