Obama set the "red line" in August, warning against any use or proliferation of the chemical weapons.
In response to Clinton's remarks, Syrian Foreign Ministry has reiterated its pledge not to use the stockpile against its own people, urging Washington to stop fabricating such claims.
"Syria has repeatedly stressed to the American side directly, or through the Russian friends, that it will not use such weapons, even if they existed, against its people under any circumstance," the Syrian ministry said, noting the U.S. made a similar claim about Iraq before it invaded the country in 2003.
Syria's stockpile is believed to include sarin nerve agent, mustard gas and cyanide.
Carney raised the prospect of the Syrian government using its chemical weapons at a White House press briefing.
"As the opposition makes strategic advances, and grows in strength, the al-Assad regime has been unable to halt the opposition's progress through conventional means," said Carney. " And we are concerned that in an increasingly beleaguered regime, having found its escalation of violence through conventional means inadequate, (it) might be considering the use of chemical weapons against the Syrian people."