Despite the widespread agreement on the issue among a politically active segment of Americans (93 percent of millionaires say they voted in the 2014 midterm elections), it may not translate into a push for action from Congress on a higher federal minimum wage.
Only 12 percent of millionaires said raising the wage should be Congress' top priority next year. The issue landed a distant fourth place behind corporate tax reform (24 percent), immigration reform (22 percent) and repealing the Affordable Care Act (20 percent).
Read MoreWhat America's millionaires expect in 2015
Along party lines, only 4 percent of Republicans and only 7 percent of Independents say raising the wage should be the top priority. For Democrats, it tied for the most important issue with immigration reform (26 percent each).
Walper maintained that the support for a higher minimum wage doesn't reflect a deep understanding of the issue's details. "The topic is extremely emotional and political, but we can't say with any degree of confidence that people understand what their state's minimum wage actually is," he said, adding, "Instead, they're responding based on what seems intuitively fair."