After Ramadi, what options does U.S. have for ISIS fight in Iraq?

But amid the doubts voiced by Carter over the determination of Iraqi troops to take the fight to ISIS, what options does the U.S. government have?

Republican Sen. John McCain laid into the Obama administration on CBS's "Face the Nation" on Sunday, blaming the White House for a deteriorating security situation in Iraq. He called on the United States to put several thousand more troops on the ground in Iraq.

"We need to have a strategy," said McCain, the chairman of the Senate Armed Services Committee. "There is no strategy. And anybody that says that there is, I'd like to hear what it is. Because it certainly isn't apparent now."

But others are wary about sending more U.S. troops back into a country where thousands of them were killed only years ago.

"I think we have to be very careful. If we do go back in, we need to understand why and what the probability of success is and exactly what we're going to do and what the limits are," said Richard Clarke, a former White House counterterrorism adviser.

Clarke told CNN that he draws the line at sending major U.S. military combat units.

"Don't put a brigade back, don't put a division back," he said. "Use special forces, use predators, use airstrikes and arm the people out there."

Currently, there are about 3,000 U.S. military personnel training Iraqi forces, but they are not near combat areas.

Some experts have called for putting some American forward air controllers who would be near the fighting to help better pinpoint the targets for coalition airstrikes.

"The problem today is we don't have anybody at the front to call in airstrikes," Clarke said. "And so our planes very often return to base with the bomb still on them."

But Carter told CNN he has not forwarded a recommendation for forward air controllers to the White House.

"If there comes a time when we need to change the kinds of support we're giving to the Iraqi forces, we'll make that recommendation," he said. "But what happened in Ramadi was a failure of the Iraqi forces to fight."

The Iraqi forces that the United States has spent billions of dollars training and equipping have so far struggled in the fight against ISIS.

At the moment, the United States is "retraining only a handful of Iraqi army brigades," according to Kenneth M. Pollack, a senior fellow in the Center for Middle East Policy at the Brookings Institution.

He called for more military trainers from the United States and other Western countries to be sent to Iraq to expand the efforts.

But Carter suggested that such efforts can only do so much.

"We can give them training, we can give them equipment -- we obviously can't give them the will to fight," Carter said. "But if we give them training, we give them equipment, and give them support, and give them some time, I hope they will develop the will to fight, because only if they fight can ISIL remain defeated."

Some analysts say what's needed to combat some of the deeper problems are "train and assist teams" embedded with the Iraqi forces.

"No one can create effective combat leaders and forces from the rear," wrote Middle East expert Anthony H. Cordesman in a post for the Center for Strategic and International Studies.

Sunni tribesman in Anbar have been at the front lines of the battle against ISIS for more than a year. But not all tribes are on the same side -- some have agreed to fight with ISIS or remain neutral.

Those who have allied themselves with the Iraqi government and the United States have repeatedly complained of a lack of support and weapons.

Iraq's Shiite-led government in Baghdad has been slow to arm the Sunni tribes. Adnan al-Assadi, a lawmaker in ex-Prime Minister Nuri al-Maliki's political block, said he and his allies oppose such a move not for sectarian reasons but to prevent such weapons from being used against the government.

"All attempts to send arms and ammunition must be through the central government, that is why we refused the American proposal to arm the tribes in Anbar," al-Assad told CNN. "We want to make sure that the weapons would not end up in the wrong hands, especially ISIS."

But such reluctance has fueled resentment among the Sunni population whose support is needed if the anti-ISIS coalition is to have any hope of rolling back the militant's gains in Anbar.

"The failure to create a Sunni National Guard and arm local tribes perpetuates the feeling among Anbar tribes that the central government lacks confidence in them," wrote Raed El-Hamed, an Iraqi researcher, in an article for Sada, a journal on Arab political issues published by the Carnegie Endowment for International Peace.

Shiite militias helped the Iraqi military wrest the city of Tikrit from ISIS in March. But analysts have expressed concern that if the militias play a major role in efforts to retake Ramadi, it could set off a downward spiral of sectarian violence.

A Shiite militia is already part of the Iraqi counterattack against ISIS underway in Anbar.

Prime Minister al-Abadi dispatched the Hashd Al-Shaabi paramilitary force -- also known as the Popular Mobilization Units -- to Anbar last week.

"The fall of Ramadi may help persuade local governments, tribal leaders ... and Sunni politicians to allow the Popular Mobilization Forces to play a role in future fights against the Islamic State," said El-Hamed.

The involvement of Iranian-backed Shiite forces also complicates matters for the U.S. military. American officials have stressed that the forces on the ground are all under the command and control of the Iraqi military to avoid a situation where Shiite militia accidentally gets hit by a U.S. airstrike.

The extreme option appears an unlikely one, even if some analysts note that the United States has less to lose than a lot of other nations.

"The fact of the matter is ISIS is a much greater threat in the region, a much greater threat to Europe than it is to the United States," Ian Bremmer, the president of the political risk research firm Eurasia Group, told CNN.

But Pollack of the Brookings Institution argues there is "no substitute" for American political and military assistance to Iraq.

"Either the U.S. does enough to pull the Iraqis through to peace and stability or the country will descend deeper into chaos and civil war," he wrote.

And a U.S. exit from the fight may not stop ISIS from targeting American interests.

"You may not want to have anything to do with them, but they'll end up having something to do with you," former British Foreign Secretary David Miliband said on CNN.