(CNN) -

In an effort to stem gun violence across the United States, President Barack Obama on Wednesday signed 23 executive actions, which don't require congressional approval -- some of which called for tougher enforcement of existing laws and required federal agencies to provide data for background checks.

He also proposed background checks on all future gun sales, as recommended by a task force led by Vice President Joe Biden. But Congress would have to approve that policy.

The term "universal background checks," used by some gun control supporters, is code for closing federal loopholes so that such checks will be conducted at gun shows and other private sales.

U.S. law requires background checks for all people who try to buy firearms from federally licensed dealers. But federal law does not require background checks for "private transactions," such as sales at gun shows. Many states have their own statutes requiring such checks for private sales.

Across the country, more than 1 million people failed background checks to buy guns during the past 14 years because of criminal records, drug use or mental health issues, according to FBI figures. That figure, however, is a small fraction of overall gun sales.

The issue has risen high in the national conversation after the shock ignited by December's mass shooting of six adults and 20 children at an elementary school in Newtown, Conn.

Expanded background checks now enjoy the support of mayors in some of the largest cities in America. The idea has been embraced by gun violence survivor Gabrielle Giffords, a self-described gun owner.

"This may be the single most important gun violence prevention measure that the government could adopt," said Lindsay Nichols, an attorney with the Law Center to Prevent Gun Violence. "This loophole means that dangerous criminals and dangerously mentally ill individuals have a most unfettered access to firearms."

But National Rifle Association President David Keene suggested to CNN's Candy Crowley that he has little faith in universal background checks, saying they don't work.

Keene spoke a few days after sitting in on the Biden task force. He implied that the task force wasn't sincerely considering NRA positions on gun control issues, saying they were simply "checking the box. They were able to say, 'We've met with the NRA. We've met with the people that are strong Second Amendment supporters.' "

The NRA reiterated that concern on Wednesday after the president held a news conference and signed the executive action.

The group touted its "efforts to promote safety and responsible gun ownership," and its "focus on keeping our children safe and securing our schools, fixing our broken mental health system, and prosecuting violent criminals to the fullest extent of the law." But it also took a thinly-veiled swipe at the president's moves.

"Attacking firearms and ignoring children is not a solution to the crisis we face as a nation. Only honest, law-abiding gun owners will be affected and our children will remain vulnerable to the inevitability of more tragedy," the NRA said.

What part of universal background checks does NRA support?

Keene did say he favored background checks to block people who may be mentally ill or potentially violent from buying guns.

But federal law already requires that, Nichols said.

One problem with the systems is that many states don't report the names of people who've been legally labeled dangerously mentally ill.

Improving the accuracy and availability of information about these people, Keene said, is one possible area for agreement. He suggested "tightening up on putting information in the database. It's school security. It's beefing up the way we deal with the mentally ill."

Nichols said "huge gaps" exist in the database, which is called the National Instant Criminal Background Check System, or NICS. For example, the Virginia Tech shooter, who killed 33 people and himself in 2007, had passed two background checks because Virginia didn't submit his mentally ill status to the database, Nichols said.

"As a result of that shooting, the federal government passed a law encouraging these states to submit these records, and a large number of states passed laws. So there's been significant improvement in reporting dangerously mentally ill persons to NICS," Nichols said. "But there are still about half of the states that report hardly any dangerously mentally ill people. They may not have the resources or the political will to enforce the law. Yeah, it's crazy."