Republican Sen. Lindsey Graham took issue with the president's calls for more gun control in his State of the Union address, saying Wednesday that the country doesn't "need a cheerleader for new gun laws."

"We need somebody to enforce the laws we have," Graham said at a press conference on Capitol Hill. "I do wish the cheerleading would stop and the prosecutions begin."

Instead of expanding background checks, Graham argued, the federal government should focus on enforcing a provision in the system that prevents individuals deemed mentally unstable from purchasing guns.

His comments came the day after Obama made and emotional plea for Congress to come up with stricter firearm legislation in order to combat gun violence. But Graham said new laws are not the way to go, though he did agree with the president that Congress should at least vote on the legislation.

"No, let's vote. No, let's vote," he said when asked if he would try to block an up-or-down vote. "I don't disagree with the president. Let's vote. Let's find something that we can agree on."

Graham stated that of the 80,000 people who failed a background check last year, only 44 were prosecuted.

He was referring to a 2012 federally-funded report about 2010 data, which stated that 76,142 background check applications were denied-about one percent of the total applications that year. Nearly half were turned down because the applicant had a record of a felony indictment or conviction, while 19% of applications were made by fugitives, and 11% ran into state law prohibitions.

Of those denied, only 4,732 cases-or about 6%--were sent to the Bureau of Alcohol, Tobacco and Firearms for investigation. The remaining 94% were not referred for investigation, or were overturned or canceled.

When an investigation is finished, the ATF and U.S. attorneys decide whether to send the case to prosecution. In 2010, a total of 62 cases were referred for prosecution, with the most common charges being falsifying information to buy firearms and being in possession of a firearm as a convicted felon or after being charged with domestic abuse.

However, 18 of those cases were dismissed, leaving 44 prosecuted.

"Mr. President, no more speeches about expanding gun laws. Start enforcing the ones we have," he said.

Asked if he thought everyone who failed a background check should be prosecuted, Graham said he assumed some people were denied because of innocent mistakes but then struggled to articulate a full response.

"But in the case of--I can give you some examples, I should have brought them with me--that if you fail the background check you're providing, you've got strawman purchases," he said. "Here's what I would suggest: Out of the 80,000, more than 44 probably did it illegally."

The senator said he was introducing his own legislation to make it more difficult for people with a history of mental instability to purchase a weapon. He acknowledged, though, that Congress will soon see "a flood of gun legislation that's going nowhere" and said lawmakers in both parties are fighting for political reasons.

"We're going to vote and people like me are going to go back to South Carolina and say I stood up for your Second Amendment rights. And my friends on the other side are going to go back to their districts and say I tried to do something about rampant gun violence. And we're all going to be talking to our bases. And at the end of the day, this problem doesn't get any more solved if all we do is talk," he said. "There's an opportunity here this time to address some areas in this emotional, real problem."

Graham added that the debate should not be solely focused on guns, adding that violence in the media, video games and mental health services should be factored into the mix.

"I've owned guns all my life. I own an AR-15. I saw the movie Django. I like Quentin Tarantino," he said chuckling. "But there are many moving parts to this....Me owning an AR-15 is not a threat to anyone because I'm not going to abuse the right to own that gun."