The public is split right down the middle on whether Obama is a strong leader, whether he is honest and trustworthy, and whether he inspires confidence.
Then there's the whole "war weariness" issue in play. Six in 10 say the war in Iraq was a mistake, and 50% say the same thing about Afghanistan. Three-quarters say the United States doesn't need to be the "world policeman."
Also hurting the president's cause, more than seven in 10 say a strike would not achieve significant goals for the United States, and a similar amount say it's not in the national interest for the country to get involved in Syria's civil war, a separate CNN/ORC International poll shows.
The sentiments come despite survey results that show 80% of Americans believe al-Assad's regime gassed its own people.
5. How the international community reacts
The next move appears to be Russia's in this diplomatic chess match. Can Foreign Minister Sergey Lavrov deliver on the offer to have Syria hand its chemical arsenal over to international control, or is it just an effort to buy time for the Assad regime?
Lavrov said Tuesday that Russia's working on a "workable, clear, specific plan" that it'll present soon.
The White House is willing to listen and, perhaps, wait a bit -- but not too long.
"It's certainly a positive development when the Russians and Syrians both make gestures towards dealing with these chemical weapons," Obama told CNN's Wolf Blitzer on Monday. But he said the threat of American force would remain.
"We don't want just a stalling or delaying tactic to put off the pressure that we have on there right now."
U.N. Secretary-General Ban Ki-moon is listening, too. He's considering asking the U.N. Security Council to demand the Syrian government immediately hand over its chemical weapons to be destroyed.
France and Germany also say they like what they're hearing about a diplomatic solution. But, the French foreign minister said, the Security Council needs to oversee the process, which should start immediately, and the plan shouldn't let anyone off the hook for ordering a chemical attack.
French Foreign Minister Laurent Fabius said Tuesday that France is proceeding with caution.
"We take note of this new position with interest but also precaution," he said. "We do not want it to be used as a maneuver for diversion."
What the French want to see is for Syria to be transparent about its chemical weapons program and to put it under international control.
France also wants the perpetrators of the deadly chemical weapons attack tried before the international justice system, Fabius said.
Iran, a longtime Syria ally, welcomes the Russian initiative "to stop militarism in the region."
China, also an ally of Syria, says it welcomes and supports the proposal.
The opposition Free Syria Army says Russia's proposal is nothing more than a stalling tactic.
"Here we go again with the regime trying to buy more time in order to keep on the daily slaughter against our innocent civilians and to fool the world," said Louay al-Mokdad, a spokesman for the group.