Sen. Charles Schumer (D-N.Y.) discussed a three-point response on Sunday to a deadly shooting in Arizona, while Sen. Tom Coburn (R-Okla.) cautioned that lawmakers should be concerned with addressing the mentally ill and not with tightening gun control laws.

Schumer, the Senate Democratic Conference Vice Chairman, would like lawmakers to examine the ability of mentally ill people to obtain guns, he said on NBC’s “Meet the Press.” He would also support legislation limiting the size of ammunition clips.

On a non-legislative front, Schumer said he is asking the Obama administration to require the military to notify the FBI when it rejects applicants on the grounds of excessive drug use.

Schumer, however, was restrained about his expectations. “Let’s be honest here,” he said. “There haven’t been the votes in the Congress for gun control.”

Jared Loughner, 22, has been charged in the Jan. 8 shooting in Tucson, Ariz. He used ammunition clips with 30 rounds, and he was able to purchase a gun despite having been rejected by the Army over his drug use.

“Now, by law, by law that’s on the books, he should not have been allowed to buy a gun” following his rejection by the military, Schumer said. “But the law doesn’t require the military to notify the FBI about that, and in this case they didn’t. So I, this morning, am writing the administration and urging that that be done, that the military notify the FBI when someone is rejected from the military for excessive drug use and that be added to the FBI database.”

Coburn rejected limiting ammunition clips and creating stricter gun control laws in general. “The problem with gun laws is they limit the ability to defend yourself, one,” he said. “But No. 2 is, the people who are going to commit a crime or are going to do something crazy aren’t going to pay attention to laws in the first place.”

He sought to keep the focus on how the nation addresses mental health. “Let’s fix the real problem: Here’s a mentally deranged person who had access to a gun who shouldn’t have had access to a gun,” he said. “Now, how do we stop that?”