I have no polling to support this, but in my experience the type of people who oppose minimum wage increases are the following:
1. Small Business Owners (and real ones, not 500-employee 'small businesses')
2. People who make a high hourly wage and are worried future raises will be affected by the min increase, OR that their hourly wages will be cut
3. People on a decent salary (or better).
A lot of times, they'll look at the minimum wage hourly and say 'well, $7.25 doesn't seem so bad.' or '$10hr is great for flipping burgers!!'. What's an easy way to counteract that?
For #1, I would simply say 'I understand, but allowing people to be paid poverty wages so that some business owners can squeak by on such a tight margin that paying their employees a few bucks more an hour will break them is not acceptable to me.'
BUT, for the other two, I believe the best way to counteract these people and their mindset is to put the minimum hourly wage in terms they'll much better relate to: what does it turn out to per-year for 40hrs/week?
$7.25hr = $15,080 gross per year, assuming they work 40 hours a week and don't miss a week.
$9.00/hr = $18,720 per year
$10.10/hr = $21,008 per year
(that's why, in these terms, $15/hr isn't nearly so offensive).
So, when it's me having this conversation with #2 or #3, I simply say this:
'Sure, I don't think the minimum wage has to be enough for one person working a full week to support a family of four. But do you know what the current wage proposals turn out to per-year, if they were salaried? (fill in the blank).
Should ANYONE not working on their own, regardless of what work they're doing, only make $21,000 a year working a full workweek, every week of the year? '