On June 1 on PBS, President Obama explained the problem: The National Rifle Association.
On June 1 on PBS, President Obama named a major obstacle in keeping guns away from suspected terrorists in this country: "The National Rifle Association." PBS

The Hill:

The FBI confirmed on Sunday it had interviewed the suspect in the Orlando, Fla., nightclub attack three times before the shooting took place early Sunday morning.

The New York Times:

The Bureau of Alcohol, Tobacco, Firearms and Explosives said Mr. Mateen had legally bought both weapons used in the attack, a handgun and a long gun, in Florida within the last week.

President Obama on June 1 at a PBS NewsHour town hall in Elkhart, Indiana:

I just came from a meeting today, in the situation room, in which I've got people who we know have been on ISIL web sites, living here in the United States—US citizens. And we're allowed to put them on the "No fly" list when it comes to airlines, but because of the National Rifle Association, I cannot prohibit those people from buying a gun. This is somebody who is a known ISIL sympathizer and if he wants to walk into a gun store or a gun show right now, and buy as many weapons and ammo as he can, nothing's prohibiting him from doing that, even though the FBI knows who that person is. So sir, I just have to say, respectfully, that there is a way for us to have common sense gun laws. There is a way for us to make sure that lawful, responsible gun owners like yourself are able to use it for sporting, hunting, protecting yourself. But the only way we're gonna do that is if we don't have a situation in which anything that is proposed is viewed as some tyrannical destruction of the Second Amendment. And that's how, too often, the issue gets framed.