Story highlights Syria is a regional conflict where causes "will persist for 10 years," Dempsey says

"We need to understand what the peace will look like before we start the war"

Washington is weighing whether to arm Syrian rebels

The administration is "going forward with a debate while events transpire," McCain says

The United States faces "a 10-year issue" in Syria as it weighs how deeply it wants to get involved the country's civil war, the top U.S. military officer warned in an interview that aired Sunday.

Army Gen. Martin Dempsey told CNN's State of the Union that the conflict is entwined in a regional issue that is now spilling over into both Lebanon and Iraq, and those underlying causes "will persist for 10 years."

"It is related -- not exclusively -- but related to a competition at best and a conflict at worse between the Sunni and Shia sects of Islam, and it's been hijacked at some level on both sides by extremists -- al Qaeda on one side and Lebanese Hezbollah and others on the other side," said Dempsey, chairman of the Joint Chiefs of Staff.

He added, "This is about a 10-year issue, and if we fail to think about it as a 10-year regional issue, we could make some mistakes."

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Syria's civil war began in early 2011, when the government of President Bashar al-Assad turned police and troops on anti-government demonstrations. The crackdown mushroomed into a conflict that has left more than more than 90,000 dead, according to the United Nations.

The Obama administration announced in June that government troops had crossed a "red line" by using chemical weapons against rebel forces, prompting it to increase what has so far been non-lethal aid to the opposition. The administration plans to send small arms, ammunition and potentially anti-tank weapons to Syria's rebels, officials familiar with the matter told CNN.

Critics such as Sen. John McCain, the ranking Republican on the Senate Armed Services Committee, call the response too little, too late.

"As usual, on these issues, they're undecided and going forward with a debate while events transpire," McCain told CBS' "Face the Nation" on Sunday. "There's no better example of that than Syria, as we continue to watch Hezbollah, thousands of fighters; we see Russian weapons pouring in, and slaughter of now over 100,000 people. And we're going to send them light weapons? Light weapons don't do well against tanks."

But Dempsey,Obama's principal military adviser, told CNN the war in Syria is "not a simple matter of stopping the fight by the introduction of any particular U.S. capability."

"It seems to me that we need to understand what the peace will look like before we start the war," he said.

What complicates the question of military support for the opposition is that many of the rebel fighters are militants with pro-al Qaeda sympathies, the same stripe of militants America has battled in Iraq and Afghanistan. They include the al-Nusra Front, a rebel group that the United States says has links to al Qaeda.