When over a million people who've been out of work for months lose their unemployment benefits tomorrow, it may actually lower the unemployment rate. But it won't only be because they suddenly were inspired to start filling out job applications and find gain employment. Instead, many people will just stop looking for work, if North Carolina's recent experience is any example.

According to November figures from House Democrats on the Ways and Means Committee, over 1.3 million people will stop receiving unemployment insurance benefits on Saturday. The Washington Post made a map of the benefits lost as a function of state population — showing that New Jersey will be the most severely affected — but the map below tells the story well enough. Heavily populated states will see more people lose their benefits. And it's mostly in blue states: about 71 percent of those losing benefits live in states that voted for President Obama in 2012.

But notice that blip in North Carolina, the bare spot. That's because the state decided earlier this year to end benefits for the long-term unemployed (defined as those out of work for 27 weeks or longer) on July 1. That move affected some 70,000 people in the state.

This is the argument that's made: people have a disincentive to find jobs because of the unemployment insurance. End the insurance, give people the incentive to work. Kentucky Sen. Rand Paul called the insurance a "disservice" to workers. And in the wake of North Carolina's move, unemployment did drop in the state. It was near 9.5 percent at the beginning of the year; now, it's around 7.5 percent.

But there isn't the direct line that people like Paul suggest. First of all, at least one study suggests that no significant disincentive actually exists. And as Business Insider reported earlier this month, yes, the unemployment rate in North Carolina dropped — but so did the size of the labor force. People in North Carolina stopped looking for jobs at a dramatic rate over the course of 2013. Since the unemployment rate is the number of unemployed divided by the size of the labor force, and since the labor force only includes people looking for jobs, the unemployment rate fell. The graph at right, via the Federal Reserve, shows the link between unemployment and labor force size in North Carolina. Blue is unemployment; red, labor force.

People in North Carolina did get new jobs, of course, but Business Insider, citing JP Morgan's chief economist, explains that this is in part thanks to "unemployed folks taking jobs for lower pay than they were waiting for." But, JP Morgan's Michael Feroli said, "the participation effect may be more important." You have to actively look for work to collect unemployment benefits, and without that push, it's easy for the long-term unemployed to lose hope.

If the benefits aren't restored nationally — a push Senate Majority Leader Harry Reid says he'll make as soon as Congress is back in session — another 1.9 million Americans could be kicked off of unemployment in the first six months of 2014. If that happens, you can expect the unemployment rate to drop. In part, because people finally got jobs. In part, because people took lower paying jobs than what they'd been expecting. And in part because people have given up, reducing the already-shrinking labor force to even lower levels.