US overreacting to Al Qaeda terror threat?

The ongoing response to a suspected Al Qaeda terror threat -- apparently emanating from the highest levels of the organization -- is also raising concerns that the U.S. might be overreacting to the intelligence, and giving away sensitive information in the process.

Officials have said they're closing embassies and consulates out of an "abundance of caution." Those precautions reached a new level on Tuesday, as the military evacuated approximately 70 U.S. personnel out of Yemen and flew them to a base in Germany. The State Department meanwhile urged all U.S. citizens in Yemen to get out if they can.

According to a senior U.S. defense official, there are about 1,400 U.S. Marines aboard Naval vessels off the coast of Yemen. They have been there for some time, but are in a position to help if needed, the official said.

The broad reaction speaks to the serious nature of the threat, which lawmakers have described as one of the most specific they've heard in years.

But some are also questioning the extent of the precautionary measures.

Daily politics news delivered to your inbox: sign up for our newsletter 

John Price, former U.S. ambassador to Mauritius, Seychelles and Comoros, told FoxNews.com LIVE that he's unclear why this particular threat is "so much in the public eye."

"We've had threats, but we never went to the media with them and we didn't deal with it the way it's being dealt with today," he said. Price said it makes sense to take additional precautions in Yemen, "because that's been the center for Al Qaeda," but questioned all the embassy closures and additional security in Africa.

"The embassies that they've closed at random in Africa don't make any sense to me," he said.

The decision to order personnel out of Yemen prompted criticism from the Yemen government. According to The Associated Press, the Yemen embassy in Washington issued a statement saying the order "serves the interests of the extremists and undermines the exceptional cooperation" between Yemen and other nations.

Former CIA officer Mike Baker said Tuesday that the tragedy of the Benghazi attack might be playing a role.

"Clearly the White House, despite calling Benghazi a phony scandal ... they're politically sensitive. They understand not just on the tragedy level but on the political level what it would mean if they have another attack and loss of U.S. life overseas or here in the States," he said.

"And so I'm afraid that there's a political calculation that has increased now in how we identify and then determine whether to release threat levels or threat alerts. And that's a problem because then that potentially drives how much information we release."

He voiced particular concern that it was leaked to the media on Monday that part of what triggered the security warnings was an intercepted communication between Al Qaeda leader Ayman al-Zawahiri and the head of Al Qaeda in the Arabian Peninsula.

"That's basically just telling Al Qaeda how we're onto them," Baker said.

There is a lot of handwringing in the intelligence community over the leak of that information, Fox News has learned. It's unclear whether the leak was authorized at higher levels or not.

Daily politics news delivered to your inbox: sign up for our newsletter 

Anthony Shaffer, a former military intelligence officer who now works with the Center for Advanced Defense Studies, said this might just be "Al Qaeda pushing our buttons" to see how the U.S. responds.

"It's a test in my judgment," he told FoxNews.com. "I think this is a trial balloon by Al Qaeda to see how we would react."

A State Department spokeswoman pushed back on that theory during Monday's press briefing.

Thomas Sanderson, senior fellow with the Center for Strategic and International Studies Transnational Threats Project, also told FoxNews.com that while an Al Qaeda trial balloon is "not beyond the realm of possibility with them," such a ruse would come with an added risk of giving away the locations of those involved.

"It's very difficult to determine what the real nature of this is," he said.

Amid the departures of U.S. personnel, militants reportedly shot down a Yemen army helicopter on Tuesday, killing eight people.

Analysts say the broad scale of the U.S. reaction -- including the closure of 22 foreign posts on Sunday and 19 posts through the end of this week, and a global travel alert -- speaks to a lack of specificity in where this attack might take place.

The evacuation operation in Yemen suggests a strong focus on the Arabian Peninsula. The Obama administration repeatedly has said the threat appears to originate in -- and possibly be directed toward -- the Arabian Peninsula, which is where Yemen is located and which houses Al Qaeda's most notorious affiliate.

The State Department said in a travel warning that it had ordered the staff departures "due to the continued potential for terrorist attacks" and added that all Americans in Yemen should leave immediately because of an "extremely high" security threat level.