This is the chart that should begin all discussions of the minimum wage, and whether we need to increase it:

That red line is corporate profits since 1970. The blue line is labor's share of income. As you can see, corporate profits are skyrocketing while labor's share of those profits is falling. This is a big part of the reason that median wages are stagnating even as the economy grows and the wealthy become ever more fabulously rich.

The problem is severe enough that it earned a mention at the beginning of President Obama's 2013 State of the Union address. "We gather here knowing that there are millions of Americans whose hard work and dedication have not yet been rewarded," he said. "Our economy is adding jobs – but too many people still can’t find full-time employment. Corporate profits have rocketed to all-time highs – but for more than a decade, wages and incomes have barely budged."

There are many explanations for why labor's share of income is falling. Globalization, automation, skills-based technological change and the decline of unions all play a part. But in the end, all these explanations end up saying the same thing: Most workers have less power to negotiate raises than they did a generation ago. And that's truest for those who making the least money and holding the fewest skills.

Economists argue over whether a small increase in the minimum wage would have no effect on employment or a slightly negative one. There's no doubt that, at some margin, making low-wage workers more expensive will lead small businesses to hire fewer of them, and lead big businesses to automate more tasks (think about the computerized checkout services that have begun popping up at CVS).

But what no one argues is that increasing the minimum wage leads, in most cases, to a higher minimum wage. If we lift the minimum wage to $9 per hour, as President Obama has proposed, then most of the workers getting paid $7.25 per hour now now will see their pay increase to $9 per hour. So these workers, who have essentially no power to bargain for higher wages, will get higher wages. That, at its base, is the case for a minimum wage hike.

There are better ways to accomplish this same goal, most of which run through the tax code. The Obama administration's first attempt was the Making Work Pay tax cut, which provided a refundable tax credit of up to $400 for working individuals and up to $800 for married taxpayers. But Republicans refused to renew it in 2011. So then the Obama administration moved to the payroll tax cut, which cuts payroll taxes by two percentage points in 2011 and 2012. But Republicans -- and some Democrats -- refused to extend it into 2013. They also expanded a variety of refundable tax credits for low-income workers -- notably the Earned Income Tax Credit and the Child Tax Credit -- in the stimulus, and those have survived.

These policies have the advantage of benefiting more than just minimum or near-minimum wage workers, and they spread their costs broadly rather than concentrating them on businesses, some of which can't afford them. In theory, an efficient way to respond to the problem of falling labor income would be to tax corporations and richer Americans and then use the money for something like the Making Work Pay tax cut. But Republicans have killed those ideas. And so the Obama administration is pushing a higher minimum wage, which isn't quite as good policy, but is much better politics.

Now, Obama's minimum wage increase might not pass the House. But if it doesn't, then Democrats have a hugely popular cudgel with which to beat Republicans in the 2014 midterm elections. That's basically what happened in the 2006 elections, and the strategy was so effective for Democrats that George W. Bush subsequently signed a minimum wage increase into law.

There's a lesson in here for Republicans. When they kill the Obama administration's more technocratic proposals but don't propose an alternative way to solve the underlying problem, they end up getting backed into a corner by his more populist proposals. That basically happened in the tax debate, where they refused to cut a big deal that included tax reform and so got stuck with a tax increase that simply raised rates. It's likely to happen here, too.