Democrats have yet another issue on which Republicans in Congress have now voted against the will of the vast majority of Americans: raising the minimum wage.

Residents gather during a minimum wage rally outside the district offices of U.S. Rep. Fred Upton, R-Mich., in St. Joseph, Mich., Tuesday, April 1, 2014 (AP Photo/The Herald-Palladium, Don Campbell)

The Senate's defeat of an increase in the minimum wage to $10.10 Wednesday-- on a near-party-line vote -- comes as upwards of three-fourths of Americans say they want to increase the minimum wage. But as with many other issues -- including gun control and immigration reform -- those national polls completely over-sell the actual electoral impact of voting against a popular proposal.

Here's why.

A Quinnipiac University poll from earlier this year showed that, while 71 percent of people supported raising the minimum wage, many of those same people said it has little to do with their vote. Just 58 percent said they would punish someone electorally for opposing the minimum wage.

As a point of comparison, that same poll showed 56 percent of people opposed Obamacare. But the vast majority -- 77 percent -- of them said they were more likely to oppose  a candidate who supported the law. Similarly, while 53 percent of people disapproved of President Obama, 81 percent of  that group said they would be more likely to vote against someone who supported him. That's what a voting issue looks like.

In other words, there is plenty of support for the minimum wage, but it's actually quite soft. And the numbers above don't even tell the whole story.

That's because the minimum wage directly affects relatively few people in the United States and Americans don't prioritize it very highly. When Gallup recently asked Americans the best way to improve the national economy, just 1 percent cited increasing the minimum wage. That ranked below tax cuts, reducing outsourcing, balancing the budget, increasing stimulus and even infrastructure spending.

In addition, the massive support for upping the minimum wage can disappear in a hurry if the debate is framed just a little bit differently. A recent Bloomberg poll showed 57 percent of people opposed the $10.10 minimum wage when informed that the Congressional Budget Office projected it would cost 500,000 jobs (while upping the wages of 16.5 million people). Just 34 percent still supported it after being informed of that fact.

Americans see the minimum wage increase broadly as the right thing to do for the working class rather than some kind of litmus-test issue -- ala Obamacare -- for candidates and incumbents. And given that American politics is all about the personal, it seems unlikely that there are gobs of voters who are just dying to punish someone who votes against increasing the minimum wage.

None of this is to say the minimum wage isn't a good issue for Democrats. It reinforces the argument that they have been making for years: Republicans favor the wealthy. When you combine the minimum wage vote with the GOP's opposition to extending long-term unemployment insurance and to upping taxes on the wealthy -- along with things like Mitt Romney's "47 percent" -- it becomes a more compelling argument. And it paid big dividends in 2012.

The minimum wage by itself, though, isn't really a 75-25 issue. In practical terms, it's probably more like 55-45.