The president says it’s no big deal if 5 percent of Americans lose their insurance because of Obamacare, yet Congress absolutely must raise the minimum wage for the 3 percent of American workers paid at that level.

OK, so that’s not exactly how President Barack Obama phrased his pivot away from the failings of his signature law and toward his preferred topic of inequality. But it’s an important starting point if we’re to understand how Obama is misdiagnosing the problem — and writing the wrong prescription.

Let’s acknowledge something up-front: Life isn’t easy for a lot of Americans right now. The prices of goods such as bread, meat and eggs have grown by double-digits over the past five years. Health insurance premiums have almost doubled during the past decade. A lot of people, especially those with the least education and lowest wages, are struggling to keep up.

But the problem is not necessarily inequality — in the president’s formulation, the difference between the top 1 percent of earners and the rest of us. It would behoove no one for everyone to be equally bad off. Likewise, the vast majority of us don’t begrudge big gains by the highest-paid as long as our lot is improving, too.

Inequality matters only if it’s blocking prosperity for everyone. That seems to be Obama’s argument, but he offers no evidence.

Oh, he did claim the typical family has seen its income rise by just 8 percent since 1979. But wherever he got that number, it doesn’t reflect reality.

According to the nonpartisan Congressional Budget Office, after-tax income for the bottom fifth of households grew by an inflation-adjusted 49 percent between 1979 and 2010. For Americans in the middle, growth was 40 percent. For those in the top fifth, minus the highest 1 percent, it was 64 percent. That’s hardly a picture of stagnation.

It’s true that the income of the top 1 percent more than tripled during the same time. But there’s no evidence this greater growth came at the expense of the rest of us. There’s only rhetoric.

(Speaking of rhetoric: Liberals love to portray the Clinton presidency as a time when government reined in “the rich” with higher income taxes. Per the CBO, it wasn’t until after Clinton was elected that after-tax income growth of the top 1 percent separated dramatically from everyone else and stayed that way.)

Looking at after-tax income is key, for a couple of reasons. First, when it comes to income, most of us care primarily about how much money we actually have to spend. Second, it tells us something important about whether the minimum wage really matters.

Just 3 percent of workers in 2011, the most recent year for which data are available, earned the minimum wage or less. That’s down from almost 8 percent in 1979. And the majority of those 3 percent don’t live in poor households (think teenage workers from middle-income families).

Even for those who do, the minimum wage isn’t all they have. Since 1980, the government has enacted the Earned Income Tax Credit as an additional — and better — way to put money in the pockets of workers who need it. The EITC, a version of policies endorsed by such conservative economists as Milton Friedman and F.A. Hayek, targets those workers who really need a financial boost.

The real obstacle to prosperity for all is the lack of jobs, especially for the least-skilled. Nothing about a minimum-wage hike, or Obamacare for that matter, addresses that problem.