"Do we have the coalition to make it work?" he asked. "You know, those are considerations that we have to take into account."
The costs of military action "have to take those into account as we try to work within an international framework to do everything we can to see Assad ousted," Obama concluded.
The crisis in Egypt
Cuomo also asked Obama about a growing congressional push to cut off over $1.2 billion in U.S. aid to the military-backed government in Egypt, where a military crackdown on supporters of deposed President Mohamed Morsy has resulted in the killing of roughly 900 people.
So far, the Pentagon has canceled upcoming military exercises and delayed the delivery of fighter jets, and is reviewing all other aspects of assistance, including military and economic help.
"My sense ... with Egypt is that the aid itself may not reverse what the interim government does," Obama said. "But I think what most Americans would say is that we have to be very careful about being seen as aiding and abetting actions that we think run contrary to our values and our ideals."
The president said the administration is currently "doing a full evaluation of the U.S.-Egyptian relationship," and that there is "no doubt that we can't return to business as usual, given what's happened."
"There was a space right after Mr. Morsy was removed in which we did a lot of heavy lifting and a lot of diplomatic work to try to encourage the military to move in a path of reconciliation," the president added. But "they did not take that opportunity."
A looming fight with congressional Republicans
Obama was slightly less diplomatic in his discussion of politics back in Washington, where a number of GOP congressional critics are spoiling for a fight this fall over the possibility of a partial government shutdown after Sept. 30 and the need to raise the federal debt limit.
Specifically, conservatives in the GOP-controlled House of Representatives are debating using both issues as leverage to force new budget cuts and defund the Affordable Care Act, the president's signature health care reform law.
"There is nobody out there who thinks that us not paying bills we've already racked up is good for the economy (or) is appropriate," Obama argued. "Nobody thinks that. So why are we even talking about?"
As for shutting down the government, that's "bad for not just people who work for the government, but all the contractors ... and the defense folks and everybody who is impacted by the services that they receive from the federal government," Obama said.
But "Republicans, after having taken 40 votes to try to get rid of Obamacare, see this as their last gasp."
The NSA and privacy concerns
Asked about the latest revelation that the National Security Agency inadvertently pulled some Americans' emails, Obama argued that the news shows "all these safeguards, checks, audits, (and) oversight worked."
Obama said he is confident no one at the NSA is "trying to abuse this program or listen in on people's email." But he said there are "legitimate concerns that people have" regarding rapidly changing surveillance technology.
"There's no doubt that, for all the work that's been done to protect the American people's privacy, the capabilities of the NSA are scary to people," Obama said.
"What I recognize is that we're going to have to continue to improve the safeguards. And as technology moves forward, that means that we may be able to build technologies that give people more assurance," he added
The Washington Post reported last week that an internal audit of the NSA found the agency had broken privacy rules "thousands of times each year" since 2008.
The 2012 audit, the Post reported, found 2,776 incidents of "unauthorized collection, storage, access to or distribution of legally protected communications" in the preceding 12 months.
The newspaper received the internal audit from NSA leaker Edward Snowden, who sparked the controversy over domestic surveillance when he first stepped forward in June.
An empty nest and a new dog
Asked about life at home at 1600 Pennsylvania Avenue, Obama said he's starting to brace himself for the day when his daughters, Sasha and Malia, head off to college.
"What I'm discovering is that each year, I get more excited about spending time with them," the president said. But "they get a little less excited" about spending time with their parents.