How is NYC preparing for potential July 4 terror threat?

Thousands of law enforcement officers in New York will spend July 4 trying to prevent a terror attack that could come from supporters of the Islamic State of Iraq and Syria (ISIS). NYPD Deputy Commissioner of Intelligence and Counterterrorism John Miller called it one of their biggest operations ever.

"I think if you look at history, they're looking at big events, they're looking at symbolic dates. They're looking at military, police, intelligence," Miller said Thursday on "CBS This Morning."

FBI and Homeland Security warn of potential July 4th terror attacks

CBS News senior security contributor Mike Morell said Monday the FBI and Department of Homeland Security's warning of a potential July 4 attack is "nothing routine."

Miller said he would not be surprised if there was an attack in the U.S. over the weekend, but said he would be surprised if it happened in New York.

"If you are a terrorist group, you're doing your assessment, you would probably pick a target that wasn't as hard when you understand what we're deploying against that," Miller said.

What they're deploying, according to Miller, is "an excess of 7,000" police officers, in addition to those patrolling the rest of the city.

"There aren't other police departments that can do that," he said.

In their effort to prevent an attack, Miller said NYPD officers are trained to look for anomalies in people's behavior, cues that distinguish a criminal from a regular spectator.

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"Somebody that's spending more time looking at security or looking out for police than they are looking at the event. Instead of looking at the front of the beautiful building, they're looking at the side entrances and where the cameras are," he said.

He also said public vigilance is critical.

"In this model our first best friend is the public, because when you put out that message, 'If you see something, say something,' and those calls come into the hotline, those are usually pretty good observations and there's a lot more of them than the police," Miller said.

But with the task of sniffing out a potential disaster amid massive crowds in New York City comes the added difficulty that the attack could come from a "lone-wolf" acting on behalf of ISIS.

"You are looking for a needle in a haystack, but the ISIS factor with the use of social media, it just makes the haystack that much bigger," Miller said. "When you're mass-marketing the idea of calling on a terrorist attack as opposed to dealing with small groups of people, that threat goes up."

Police officers control the crowd after a gunman opened fire on a beachside hotel in Sousse, Tunisia, June 26, 2015. Amine Ben Aziza/Reuters

Last month, ISIS urged its followers "to make Ramadan a month of calamities for the nonbelievers."

Three attacks, all on the same day, followed soon after the call to arms. ISIS claimed responsibility for both the deadly explosion at a mosque in Kuwait's capital city and the massacre at a hotel in Sousse, Tunisia. Reports reveal that the man who carried out an attack and beheading at a U.S.-owned industrial chemical factory in Lyons, France, that same Friday may have also had ties to ISIS.

"When you see the simultaneous attacks this week in those three countries, when you see that each one was markedly different in terms of tactics and procedures, when you see ISIS claiming credit, and we're still assessing this, for a series of simultaneous attacks against military targets in the Sinai, what you're seeing is an organization that is starting to develop a complex external operations attack that goes beyond calling for attacks on social media, but actually running them and having them train people in advance," Miller said.

There are over two weeks left in the holy month of Ramadan -- something Miller said "you have to factor in" when assessing the July 4 terror threat.

"They've made the calls before and people have acted on them," he said.