Will the U.S. start bombing ISIS in Syria, too?

That's the question raised by a report Tuesday from the Associated Press that says the U.S. has already started flying surveillance missions over Syria to gather intel on ISIS militants there.

Earlier this month, Obama ordered airstrikes against ISIS militants in Iraq. Yet those assaults were aimed at rescuing trapped refugees and pushing ISIS back from Iraq's largest dam.

Shifting the bombing campaign across the border into Syria would represent a sharp escalation in the fight against ISIS, and it would muddle an already complicated foreign policy picture. The U.S. accused Syrian President Bashar al-Assad of using chemical weapons on his own people, and three years ago President Obama insisted Assad must step down. Attacking ISIS, who have waged war with Assad's forces, would de facto aid the embattled Syrian leader.

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Still, the administration seems resigned to that possibility, with Chairman of the Joint Chiefs of Staff Gen. Martin Dempsey saying last week the U.S. may need to attack ISIS "on both sides of what is essentially at this point a non-existent border."