President Obama has authorized initial U.S. planning for possible intervention in Syria, but the lack of unity within the Syrian opposition and the international community currently argue against such a mission, top U.S. defense officials said Wednesday.

“There are no simple answers,” Defense Secretary Leon E. Panetta told a contentious Senate Armed Services Committee hearing on Syria. “The result is a great deal of anger and frustration that we all share.”

Testifying with Panetta, Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, told lawmakers a “commanders’ estimate” has been discussed with Obama and the National Security Council, including assessments of “potential missions, the enemy order of battle,” how much time it would take and “the troops we have available.”

Panetta said that “we have not done the detailed planning because we are waiting for the direction of the president to do that.”

Obama said Tuesday that military intervention at this point would be “a mistake” and warned against “the notion that the way to solve every one of these problems is to deploy our military.”

Even as Republicans have accused Obama of offering a weak response to Syrian President Bashar al-Assad’s onslaught against civilian opponents, and some have called for U.S. airstrikes, “others are concerned about the dangers of involving ourselves in yet another conflict in that part of the world,” Panetta said.

The hearing followed earlier Senate testimony by Gen. James Mattis, head of the Central Command, that Assad’s forces are “gaining physical momentum on the battlefield” and that the slaughter of civilians will “get worse before it gets better.”

Sen. John McCain (R-Ariz.) has led the call for the United States, ideally acting with allies, to begin airstrikes in Syria to stop the carnage. “How many more have to die — 10,000 more, 20,000 more?” he asked Panetta and Dempsey.

But Dempsey said the attacks necessary to destroy Syrian air defenses would be long, complicated and risky because the systems are five times more sophisticated than those attacked by the NATO-led coalition in Libya last year.

“It would take an extended period of time and a great number of aircraft,” Dempsey said. Because most Syrian air defenses are located in the heavily populated western part of the country, where most of the violence against opposition strongholds is taking place, civilian casualties and other collateral damage would be high, he said.

The “next level of detail,” following the commanders’ estimate, should Obama request it, would be “for us to take actual units, from someplace else, applying them against that template in order to come up with operational concepts,” Dempsey said. “How would we do it?”

Any U.S. action in Syria, he said, would be a “zero sum game” that would require military assets transferred from other missions.

Right now, Panetta said, the administration is trying to build international consensus. “What doesn’t make sense is to take unilateral action at this point,” he said. “Before I recommend that we put our sons and daughters in uniform in harm’s way,” the United States needs to “make very sure we know what the mission is, whether we can achieve that mission, at what price, and whether or not it will make matters better or worse.”

Panetta outlined four goals of current policy, including increasing Assad’s diplomatic and political isolation with international sanctions that he said were “having a significant impact.”

With international partners, he said, the United States is also providing emergency humanitarian assistance to the Syrian people and “working with the friends of Syria to help strengthen the opposition, try to encourage various opposing groups to unify, and lay the groundwork for a peaceful, orderly transition to a democratic government.”

Finally, he said, “we are reviewing all possible additional steps that can be taken with our international partners to support the efforts of the Syrian people to end” the violence, “including potential military options if necessary.”

He said Obama had directed him to raise the question with NATO of possible alliance involvement. NATO Secretary General Anders Fogh Rasmussen has said that NATO will not participate in any action in Syria.

“The fundamental issue before us is whether or not the United States will go ahead and act unilaterally in that part of the world and engage in another war in the Muslim world unilaterally,” Panetta said, “or whether we will work with others. ... That is the fundamental decision we have to make.”

He acknowledged that some Persian Gulf countries, reportedly Saudi Arabia and Qatar, are already planning to supply weapons to the Syrian opposition. He said the administration was in consultation with them.

Panetta also confirmed that preparations have been made to supply communications and other “non-lethal” equipment to Syrian opposition forces. But for the moment, he stressed, the opposition is divided into “approximately 100 groups that we’ve identified.”

He said U.S. intelligence believes that although al-Qaeda is trying to exploit the opposition, “we’re not suggesting that part of al-Qaeda has aligned itself or is in bed with the opposition.” But one of the many problems in arming the opposition, Panetta said, is “not how quickly we could vet them all but how quickly we could vet enough of them that could form a coherent whole” that “doesn’t exist today.”

“Despite our aspirations and hopes,” he repeated, “it doesn’t exist.”

Some committee Republicans said that the United States should take the lead in Syria, both on moral grounds and because of the acknowledged strategic loss Assad’s fall would mean for Iran, its main ally in the region.

Others sharply criticized Russia, whose veto, along with China’s, has quashed two United Nations Security Council resolutions.

In a particularly testy exchange, Sen. Jeff Sessions (R-Ala.) questioned Panetta’s observation that the United States would need a legal basis for intervention that would include obtaining “permission” from the United Nations or NATO.

“I want to make sure the U.S. military understands that we’re not dependent on a NATO resolution or a U.N. resolution to execute policies consistent with the national security of the United States,” Sessions said. “Are you saying the president is taking the position that he would not act if it was in our interests to do so if the U.N. Security Council did not agree?”

At that point, Sen. Carl M. Levin (D-Mich), the committee chairman, intervened. “I want to clarify,” Levin said. “You used ‘permission’ ” in terms of “being helpful to achieving an international coalition. You don’t need authority, permission from anybody else if we’re going to act alone.”