On the eve of President Obama's speech laying out his strategy to combat the terror group ISIS, national security hawks are demanding the United States authorize airstrikes against the group's leaders.

"We need to be targeting the top ISIS military and strategic leadership," said Danielle Pletka at the American Enterprise Institute. "Our policy up 'til now hasn't been good enough. It's a day late and a dollar short, and that's why ISIS is a threat to the United States."

So far, U.S. airstrikes have focused on ISIS field positions in Iraq, following three limited goals outlined by the President: to protect Americans, help Iraqi forces and prevent a humanitarian disaster. But top leaders have not been singled out, according to Pentagon spokesman Col. Steven Warren. "We have not conducted any targeted airstrikes on specific ISIL leaders," he said, using the administration's acronym for ISIS, which calls itself the "Islamic State".

Still, when asked why the United States is not trying to kill the group's top leaders, White House spokesman Josh Earnest did not rule out such a strategy in the future.

"I would anticipate that as our intelligence improves, and crystallizes, that our military capabilities will expand accordingly," Earnest said Tuesday. Moreover, he said, thanks to the formation of a new Iraqi government, the President believes "we are ready to enter the next, more offensive phase, in this strategy."

The President's former national security adviser, retired Gen. James L. Jones, said he would be very surprised if the President did not instruct the military to target the head of ISIS at some point.

"When the President gives the word, it will be a formidable capability that we launch against this organization, and perhaps against him."

Analysts said the first challenge would be to locate elusive ISIS leaders like Abu Bakr al-Baghdadi.

"The trouble is, they don't have good human intelligence networks in Syria right now," said Paul Cruickshank, author of a new book about a mole who infiltrated al Qaeda. Trying to penetrate a group as ruthless as ISIS with a secret agent would not only be extraordinarily difficult, he said, but also highly dangerous.

Former CIA operative Robert Baer said he believes ISIS militants are shrewdly avoiding electronic intercepts. "I'm quite certain that ISIS is staying off the phone, and nobody around Baghdadi, for instance, would have a cell phone, for instance, or any kind of communications," he said. And the failure of the recent U.S. attempt to rescue American hostages with a team of commandos, he said, showed that "our information is old, and secondhand."

(CNN)