AP Fact Check: GOP Claims on Health Plans, China, Economy

Ted Cruz spoke of millions losing health coverage - but more than 16 million people have gained it, shrinking the pool of uninsured like never before. Donald Trump laid roughly the entire U.S. trade deficit at the feet of China, botching the numbers. Chris Christie overlooked pay gains for construction workers in a lunch-pail tale meant to slam President Barack Obama.

Some twisted stories emerged from the latest Republican presidential debate and Donald Trump's competing rally in Iowa.

A look at some of the claims Thursday night and how they compare with the facts:

CRUZ: "We have seen now in six years of Obamacare that it has been a disaster. It is the biggest job-killer in this country. Millions of Americans have lost their jobs, have been forced into part-time work, have lost their health insurance, have lost their doctors, have seen their premiums skyrocket. "

THE FACTS: Lost jobs? Since the time Obama signed the health care law in March 2010, the nation's jobless rate has fallen from 9.9 percent to 5 percent. The economy has added more than 13 million jobs over that period.

Lost insurance? The share of Americans without coverage reached a historic low of 9 percent last year, according to the government's National Health Interview Survey. More than 16 million people gained coverage since 2013, just before the law's big coverage expansion got underway.

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TRUMP: "China this year in trade will make over $500 billion dollars in terms of our trade deficit. $500 billion. That's no partnership, and I'm a free trader. I love free trade. But we have to use our head. And we use political hacks to negotiate with the Chinese."

THE FACTS: Trump should re-check his numbers before conducting a trade negotiation. He could be referring to the total U.S. trade deficit with every country in the world. That totaled about $508 billion in 2014, which actually represents an improvement from the $762 billion deficit reached in 2006, according to the Census Bureau.

But the trade deficit in goods with China was $343 billion in 2014 - significantly below what Trump has suggested in multiple statements.

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MARCO RUBIO: "You cannot destroy ISIS with a military that's being diminished."

CRUZ: Obama has "dramatically degraded our military.

"THE FACTS: The charge that President Barack Obama has starved the Pentagon has become a refrain in the GOP primary campaign, but amounts spent on weapons modernization are about the same as they were when Republican George W. Bush was president.

Any military cuts GOP contenders are complaining about were approved by both Republicans and Democrats in Congress. The military budget is being squeezed by the insistence of lawmakers in both parties that money be spent on bases and equipment that the Pentagon says it doesn't need.

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CRUZ on Obama: "He's not arming the Kurds."

THE FACTS: He is. The U.S. has allocated a substantial amount of weapons and other military equipment to help the Kurds fight the Islamic State group, and is sending the aid.

The shipments have not been direct. Rather, under a deal with the Iraqi government, all U.S. weapons sent to help in the fight are delivered to Iraqi officials, and they divide the weapons between Iraqi and Kurdish forces.

It's true the Kurds have complained that the assistance is not enough. But they are getting arms and other equipment from Washington.

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CHRIS CHRISTIE: "For the 45-year-old construction worker out there, who is having a hard time making things meet, he's lost $4,000 in the last seven years in his income because of this administration."

THE FACTS: There may be some in hard hats who've lost income, but on the whole, construction workers are faring much better than they did when Obama first took office.

The latest federal jobs report showed their average weekly earnings have risen 2.7 percent annually since 2009 - much faster than the national average for non-management employees. Their weekly earnings jumped to $1,021 in December, compared with a weekly income of $858 seven years ago.

Certainly not everyone has prospered. Overall, the median household income has dropped since 2009 by $1,268, to $53,657.

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CRUZ defending his threat to "carpet bomb" Islamic State fighters: "It's what we did in the first Persian Gulf War."

THE FACTS: The U.S. conducted an intensive air war against the Saddam Hussein government in the 1991 war. But to call it "carpet bombing" misses one of the most important characteristics of that air campaign: It marked the first large-scale use of precision-guided missiles and bombs in the history of warfare.

That war also saw the first substantial combat use of the Air Force F-117 stealth fighter, which made it possible for the U.S. to lower risk to pilots flying against enemy air defenses while delivering precision weapons.

The driving force behind developing precision-guided munitions, which today are even more precise than 25 years ago in the Persian Gulf war, was the goal of reducing the risk of killing civilians. It's a goal the U.S. military has embraced under Republican as well as Democratic presidents.

And Cruz has not explained how carpet bombing a terrorism group that is mingled with citizens in areas they control can be done without substantial deaths of innocents.

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RUBIO: Asked to reconcile his past opposition to granting amnesty for people in the United States illegally and his sponsorship of a bill that would grant those people a path to U.S. citizenship, he said "We're going to keep ISIS out of America" and "enforce our immigration laws."

CRUZ: Asked to reconcile his vocal backing for the same bill (along with his attempt to improve its chances with an amendment), and his current claim to never have supported it, said; "The fact that each amendment didn't fix every problem didn't mean that I supported the rest of the bill."

THE FACTS: About the only thing that was clear in this exchange is that both are squirming over their past immigration positions in a primary season dominated by conservative voters.

For Rubio, there was one fact on the stage that he couldn't escape - fellow candidate Jeb Bush verified that Rubio asked him to support his path-to-citizenship legislation when it was being written in 2013. And Cruz was caught by a video clip of himself on the Senate floor, urging the bill's passage.

Both tried to dismiss their previous statements and emphasize their current stance of wanting to secure the nation's southern border before any other actions are taken to address immigrants living in the country illegally.