The Obama administration’s efforts to justify the National Security Agency’s vast data-gathering about Americans’ phone and online communications hit a snag this week, as doubts surfaced about newly declassified details on terrorism investigations that U.S. intelligence officials released to reassure the public.

Lawmakers with access to classified information and lawyers who have followed the four cases made public said the NSA’s domestic data gathering had not played the crucial role that officials assert.

“We have yet to see any evidence that the bulk phone records collection program has provided any otherwise unobtainable intelligence,” Democratic Sens. Ron Wyden of Oregon and Mark Udall of Colorado said in a joint statement.

“It is highly doubtful that these [NSA collection] programs played the kind of central role in these cases that officials have said,” said Michael German, a lawyer and former undercover FBI agent who now works for the American Civil Liberties Union.

Since contract computer technician and self-proclaimed whistleblower Edward Snowden revealed the existence of two huge top-secret NSA data-gathering programs this month, officials have struggled to justify them to the public without worsening the damage they say the revelations have caused to national security.

This week, intelligence officials at a rare public hearing told the House Permanent Select Committee on Intelligence that more than 50 terrorist plots, 10 to 12 of which involved a target in the U.S., had been foiled using intelligence from at least one of the NSA programs.

One of them, which uses a computer system called Prism to get real-time access to electronic communications carried by U.S. Internet and technology companies, is authorized under Section 702 of the Foreign Intelligence Surveillance Act (FISA) amendments of 2008.

Prism, which allows the NSA to eavesdrop on email and text messages, as well as Internet telephone and video chat services such as Skype, is used only against targets “reasonably believed” to be foreigners outside the U.S., officials say. They acknowledge that some Americans’ communications are collected “inadvertently” because they are in touch with targeted suspects.

But there has been more concern about the second program exposed by Mr. Snowden, which is authorized under Section 215 of the USA Patriot Act, a large suite of anti-terrorism laws passed hurriedly in the wake of the Sept. 11, 2001, terrorist attacks.

Under this program, the NSA collects so-called metadata — time, duration and destination number — about every telephone call made in the U.S. Officials told the House intelligence committee that the data helped them identify contacts between terrorists abroad and their associates in the U.S.

But even FBI Director Robert S. Mueller III acknowledged Wednesday that this huge NSA database of domestic phone calls was only “a contributing factor; one dot amongst a number of dots,” in “many” of the 10 to 12 cases involving a planned attack in the U.S.

The one case that he said wholly relied on the program was a 2003 probe that began after a tipoff about a San Diego-based supporter of al-Shabab, a Somali terrorist group with links to al Qaeda.

“We closed the investigation down,” said Mr. Mueller, explaining that agents were unable to find evidence of a terrorist connection.

In 2007, the NSA gave the FBI a phone number in San Diego that they said had been in contact with a phone in East Africa they were monitoring.

“They could not tell what calls were made to that telephone line in East Africa,” said Mr. Mueller. “And consequently, they took that number, ran it against the database and came up with this telephone number in San Diego.”

Officials then had to “go through the additional legal process” to get the name of the phone subscriber, ensure that there was “predication,” meaning sufficient grounds to open a full federal investigation, and obtain a warrant for a wiretap.

On the basis of that surveillance, four men were convicted this year of fundraising for al-Shabab.

“That is one case where you have [Section] 215 [data-gathering authority] standing by itself,” Mr. Mueller told Senate Judiciary Committee Chairman Patrick J. Leahy, Vermont Democrat.

But Mr. Wyden and Mr. Udall, the two Democrats who have seen classified information about the cases, said Mr. Mueller and other officials were giving credit to Section 215 domestic collection for foiling plots that actually were thwarted using foreign intelligence programs such as Section 702.

“Saying that ‘these programs’ have disrupted ‘dozens of potential terrorist plots’ is misleading if the bulk [domestic] phone records collection program is actually providing little or no unique value,” they said in their statement.

In fact, the ACLU’s Mr. German said, the huge proliferation of electronic surveillance data was overwhelming the FBI and “just making the haystack bigger.”

He noted as an example of missing a needle that the FBI’s Webster Commission Report into the bureau’s failure to identify accused Fort Hood shooter Maj. Nidal Hasan as a jihadist called the case “a stark example of the impact of the data explosion.”

“The exponential growth in the amount of electronically stored information is a critical challenge to the FBI,” the commission concluded.

Also Thursday, the FBI acknowledged that Deputy Director Sean Joyce misspoke this week in describing to lawmakers details about another of those four cases, involving a Kansas City man called Khalid Ouazzini.

Mr. Ouazzini was placed under court-ordered surveillance by the FBI after the NSA discovered he had been in email contact with a terrorist suspect in Yemen, Mr. Joyce said. He added that the surveillance uncovered a “nascent” plot to bomb the New York Stock Exchange.

“Was the plot serious?” he was asked.

“I think the jury considered it serious, since they were all convicted,” he replied.

But an FBI official acknowledged Thursday that Mr. Ouazzini and two associates in New York had merely pleaded guilty to lesser charges of money laundering or providing support to terrorist groups.

Nevertheless, the official defended that case as an example of the program’s success regardless of the specific convictions ultimately achieved.

“We stand behind the example that was provided,” he said.

Nonetheless, doubts continued to surface about the other two cases as well. In the case of David Headley, the Pakistani-American charged with aiding the 2008 Mumbai terrorist attack, the ACLU’s Mr. German said the FBI had received “no fewer than five separate tipoffs that he was visiting terror training camps — two of them from his ex-wives.”

Authorities said Headley was planning an attack on the Danish newspaper that printed multiple satirical cartoons of Islam’s Prophet Muhammad when the NSA program enabled officials to catch up to him.

The most serious attack officials say was thwarted was Najibullah Zazi’s attempt to bomb the New York subway. Zazi was caught because his al Qaeda handler in Pakistan was emailing him from the same Yahoo account that he had used to communicate with a British-based terrorist cell broken up the previous year, official said.

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