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Obama said gun owners would support his new restrictions. He was right.

At a town hall event on Jan. 7, President Obama outlined his executive action on gun control and answered questions from the audience. (Video: CNN)

President Obama rolled out a package of executive actions on guns this week. The changes included clarifying rules meant to broaden the use of background checks by private sellers, allocating money for mental health treatment, and adding more staff at the FBI and the Bureau of Alcohol, Tobacco, Firearms and Explosives to help enforce existing regulations.

The changes were modest in scope -- experts and even the NRA agreed that their overall impact would be small. That didn't stop Obama's critics from fiercely denouncing the proposals. But the president predicted the public would be on his side. The actions would be supported by an "overwhelming majority of the American people, including gun owners," he said Monday.

As it turns out, he was right.

A new CNN-ORC survey of 1,000 Americans finds that the public supports Obama's plan by a 2-to-1 ratio: 67 percent of respondents favored the executive actions, while 32 percent opposed them. Even more striking, a similar share of people in gun-owning households -- 63 percent -- supported the measures.

Even more striking: 51 percent of Republicans support Obama's executive action on guns. When's the last time 51 percent of Republicans agreed with Obama on anything?

Consider, also, the question wording: "As you may know, this week Barack Obama announced several executive orders that change the nation's gun laws so that background checks are required for more purchases online and at gun shows, and which make it easier for the FBI to complete background checks efficiently. Overall, do you favor or oppose these changes?"

We know that attaching a politician's name to a survey question can greatly influence partisan responses to the question. In a recent YouGov polling experiment, for instance, 16 percent of Republicans agreed with the notion of universal health care when told that Obama agreed with it. When a separate group of Republicans was told instead that Donald Trump agreed with universal health care, support jumped up to 44 percent.

So the fact that 51 percent of Republicans agreed with Obama's gun actions, even when told that Obama was the one proposing them, is pretty significant.

In the end, like so many gun policy proposals -- universal background checks, a federal database of gun sales, barring people with mental illness from buying guns, prohibiting gun ownership for domestic abusers, prohibiting gun sales to people on the terrorist watch list -- Obama's executive actions are supported by a strong majority of the public and of gun owners.

But there's a small minority of citizens -- led by the leadership of the NRA and its allies in Congress -- who vehemently oppose any additional restrictions on gun access. This group of people also happens to be very vocal, and they've done a great job of convincing the media and the public that their numbers are larger than they really are.