This morning, after Mitt Romney proclaimed in his announcement speech yesterday that Obama’s policies made the recession “worse,” the Associated Press published a bracing fact-check skewering the claim:

ROMNEY: “When he took office, the economy was in recession. He made it worse. And he made it last longer.”

THE FACTS: The gross domestic product, the prime measure of economic strength, shrank by a severe 6.8 percent annual rate before Obama became president. The declines eased after he took office and economic growth, however modest, resumed. The recession officially ended six months into his presidency. Unemployment, however, has worsened under Obama, going from 7.8 percent in January 2009 to 9.1 percent last month. It hit 10.1 percent in October 2009.

A case can be made for and against the idea that Obama’s policies made the economy worse than it needed to be and that the recession lasted longer than it might have under another president. Such arguments are at the core of political debate. But Obama did not, as Romney alleged, make the economy worse than it was when he took office.

Yet barely minutes later, in response to the bad jobs report this morning that found that hiring slowed sharply in May, Romney released another statement making the same debunked claim again:

“Today’s unemployment numbers show that we are going backwards, and that is the wrong direction for America. President Obama’s policies made the recession worse and as a result more people are out of work. These unemployment numbers should not be viewed as just statistics — these are real families facing significant economic peril because President Obama has failed to pull us out of this economic downturn. Americans deserve a president who will make job creation his number one priority.”

This is not the first time this has happened with Romney. During his announcement speech yesterday, he repeated the claim that Obama has “apologized for America,” even though it has been thoroughly, completely, decisively debunked.

What you’re seeing here the limitations of fact-checking, and it’s something we rediscover during every presidential campaign. Candidates make false claims; media fact-checkers go to work and debunk them; the candidates go right on making them anyway; reporters weary of pointing out that they’re false and they start making their way into stories with no rebuttal.

There’s no denying that the new jobs numbers are terrible, and that this is very bad news for Obama and Democrats politically, which is why it’s understandable that Romney would pounce on them. But it’s now clear that Romney is going to make the claim that Obama made the recession “worse” a core message of the campaign — an assertion that goes beyond the debate over jobs numbers and right to the heart of the argument over the efficacy of Obama’s policies. And as the Associated Press points out, according to the prime measure of economic strength it’s demonstrably false. Will reporters press him to explain himself if he keeps making this claim? Will media outlets take a stand on whether it’s false every time he makes it?