The military is prepared to deploy the bombs, which contain the precursor chemicals for the deadly sarin nerve gas, from dozens of fighter-bombers as soon as Assad gives the order.
Sarin is classified as a weapon of mass destruction by the United Nations, and its production and stockpiling is outlawed under the 1993 Chemical Weapons Convention.
But a U.S. official speaking to NBC News on condition of anonymity said the nerve agents are now locked and loaded inside the bombs and "there's little the outside world can do to stop it" if Assad gives the go-ahead.
Clinton, speaking Wednesday at NATO's Brussels headquarters, called Assad "increasingly desperate."
"Ultimately, what we should be thinking about is a political transition in Syria and one that should start as soon as possible," Clinton said. "We believe their fall is inevitable. It is just a question of how many people have to die before that occurs."
Syrian forces earlier Wednesday pressed a counteroffensive against rebels near Damascus as a report indicated the regime army was weakening against rebel gains.
Western officials and military analysts told The Washington Post the Syrian army was showing serious cracks as emboldened rebels notched new victories and regime forces retrenched.
Opposition troop successes stem, in part, from funding and weapons from wealthy Arab Persian Gulf donors and Syrian businessmen outside the country, the Post said.
They also reflect the degraded state of the Syrian army, which appears low on supplies and morale, analysts told the newspaper.
Troops loyal to Assad and rebel forces clashed in several southern Damascus suburbs where rebels have scored several tactical victories in recent days, the Syrian Observatory for Human Rights said.
They also fought as opposition troops advanced toward Damascus International Airport, the British-based Observatory said.
Rebels and regime forces also clashed around the strategically important Wadi al-Deif military base near the northwestern city of Maarat al-Numaan that earlier saw Syrian jet fighters bombing attacking rebels, activists said.
The fighting came a day after a mortar attack on an elementary school 10 miles north of Damascus killed at least 15 people and perhaps 30.
The official Syrian Arab News Agency said the attack on the school in the Wafideen refugee camp killed 14 students and a teacher, while opposition Local Coordination Committees network said 30 students were killed.
The camp houses Syrians displaced from the Golan Heights in 1967 when Israel occupied the territory.
SANA blamed the attack on "terrorists," its term for rebel fighters. The Local Coordination Committees said the Assad regime was to blame.
At a meeting in Brussels, NATO ministers expressed "grave concern" about reports the regime might be getting ready to use chemical weapons.
NATO Secretary-General Anders Fogh Rasmussen warned the regime any use of chemical arms would meet an "immediate" international response.
The ministers, including Clinton, later agreed to deploy Patriot surface-to-air missiles in Turkey, which had requested the installations as a defense against cross-border violence after learning Syria contemplated using the chemical weapons.
Separately, former Syrian Foreign Ministry spokesman Jihad Makdissi was on his way to the United States after apparently defecting, Britain's The Guardian reported Wednesday.
Makdissi, the most senior Christian official to abandon the Assad regime, was en route to an unidentified U.S. destination or had already landed after managing to leave Damascus for Beirut, the newspaper said.
He did not travel to Britain, British officials said, denying earlier reports.
In Washington, a State Department spokesman said, "We are not in a position to confirm his actions or whereabouts."
Lebanon's al-Manar satellite television reported Monday Makdissi was fired for making statements that did not reflect the regime's position. Makdissi said in July Syria would use chemical weapons only against a foreign invasion. Syria prefers not to acknowledge having chemical weapons.