Sen. Chuck Schumer (D-NY) said Sunday that Congress lacks the necessary votes to stiffen gun laws, dampening the hopes of various gun-control bills proposed in the aftermath of the Arizona shootings.

"Let's be honest here -- there haven't been the votes in the Congress for gun control," Schumer said on NBC's "Meet the Press," calling it a "hard" issue.

Schumer, the third-ranking Democrat in the Senate, nevertheless spoke out in favor of "smart, rational gun control laws that protect the right to bear arms, but have reasonable limits."

"There is a right to bear arms. It's in the Constitution. And you can't ignore it, just like you can't ignore the others," he said. "But like all the other rights, it's not absolute."

Schumer did, however, propose stronger sharing of communication between the military and the FBI, which he argued would have turned up a red flag on Tucson shooter Jared Lee Loughner when he attempted to buy a gun.

Since Loughner's shooting rampage last Saturday that killed six and injured thirteen, including Rep. Gabrielle Giffords (D-AZ), members of both major parties last week introduced bills to clamp down on gun and ammunition sales.

But the difficulty such measures continue to face is a testament to the influence of pro-gun interests. The National Rifle Association, often described as Washington's most powerful lobby, spent over $2 million lobbying in 2010, according to the Center for Responsive Politics.

On "Meet the Press" Sunday, Sen. Tom Coburn (R-OK) spoke out against toughening gun laws, arguing that doing so would not prevent future atrocities and would impede with rights to self-defense.

"If you have somebody that is a criminal, that wants to get around the law, they're going to get around the law," Coburn said. "The problem with gun laws is they limit the ability to defend yourself, one. But number two is, the people who are going to commit a crime or going to do something crazy aren't going to pay attention to the laws in the first place."

Rep. Carolyn McCarthy (D-NY) announced plans for a measure restricting the buying and selling of high-capacity ammunition magazines, like the one purchased legally and used by 22-year-old Jared Lee Loughner in Tucson. Sen. Frank Lautenberg (D-NJ) has backed the proposal.

Rep. Gary Ackerman (D-NY) introduced a bill to close the "fire sale loophole," though which unauthorized gun dealers can sell firearms at gun shows to buyers who can bypass an otherwise mandatory FBI background check.

Rep. Peter King (R-NY) put forth legislation seeking to ban guns carried within 1,000 feet of members of Congress. House Speaker John Boehner (R-OH) and Majority Leader Eric Cantor (R-VA) opposed the idea.

The United States has the largest rate of per capita gun deaths among wealthy nations, and also has some of the most lenient gun laws.

The Tucson massacre has triggered a spike in sales of semi-automatic pistols in Arizona, gun dealers said.

The following video is from NBC's "Meet the Press," broadcast Sunday, Jan. 16.

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