By Carlo Muñoz - 06/26/13 08:42 PM EDT
But those concerns seem to have fallen on deaf ears among several defense hawks in Congress.
Sens. John McCain (R-Ariz.), Carl Levin (D-Mich.), Lindsey Graham (R-S.C.) and Bob Menendez (D-N.J.) all want Obama to put military pressure on the Syrian regime by creating a no-fly zone and launching air strikes against the country's defenses.
Levin, the chairman of the Senate Armed Services Committee, said it was “essential” that the U.S. “step up the military pressure on the Assad regime.”
Dempsey reiterated the Pentagon's standing concerns on Wednesday.
"It will be difficult because the Syrian air defense system is sophisticated and it's dense," he said.
That said, "if that is a decision that the nation takes that we want to impose a no-fly zone, we'll make it happen," Dempsey added.
American military leaders have reportedly drafted strategic plans for a possible no-fly zone in Syria, located along the country's shared borders with Turkey and Jordan.
U.S. military advisers are working closely with the Jordanian military to address a number of regional security concerns, including Syria.
CIA operatives and U.S. special operations troops have also been training Syrian rebels in Turkey since late last year on using anti-tank and anti-aircraft weaponry, according to recent news reports.
Defense Secretary Chuck Hagel also recently approved a request from Amman to keep a detachment of Air Force F-16s and a Patriot anti-aircraft missile battery in Jordan.
Earlier this year, then-Defense Secretary Leon Panetta ordered a Patriot missile battery to be deployed along Turkey's border with Syria.