The Senate is expected to take its first vote on Wednesday, a procedural matter that could give an early indication of how much support Obama has.
Asked about his chances of convincing a skeptical Congress to give its stamp of approval to a limited attack, Obama said, "I wouldn't say I'm confident."
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But he added, "I'm confident that the members of Congress are taking this issue very seriously and they're doing their homework and I appreciate that."
Syrian President Bashar Assad has warned that the U.S. should expect retaliation for any air strikes, but Obama said that should not sway Congress.
"Syria doesn't have significant capabilities to retaliate against us. Iran does, but Iran is not going to risk a war with the United States over this,"Obama said. "Particularly given that our goal here is to make sure that chemical weapons are not used on children."
'Skeptical' of Russian-Syrian proposal
He also expressed wariness about a new Russian proposal — "welcomed" by Syria's foreign minister — to have Damascus turn over its chemical weapons to international inspectors.
"I think you have to take it with a grain of salt initially," he said. "This represents a potentially positive development. We are gonna run this to ground.
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"I think what we're seeing is that a credible threat of a military strike from the United States, supported potentially by a number of other countries around the world, has given them pause and makes them consider whether or not they would make this move," he added.
"And if they do, then this could potentially be a significant breakthrough. But we have to be skeptical because this is not how we have seen them operate over the last couple of years."
Asked about his reaction to the graphic videos of Syrian civilians killed in last month's chemical-weapons attack — which the White House has used to persuade Congress to back a strike — Obama said he was "heartbroken."
"I would recommend everybody look at these videos," he said.
He emphasized that U.S. strikes would be "limited" but effective.
"Look, nothing is 100 percent guaranteed in life," he said. "But I think it's fair to say that our military is outstanding, our intelligence is outstanding, and we have shown ourselves capable of taking precision strikes on military installations in ways that would degrade Assad's capabilities to deliver chemical weapons — that would have a significant impact, but that would not lead to escalation."
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Obama also used his wife as a stand-in for John Q. Public in noting that he realizes the American people are reluctant get involved in yet another conflict.
"And if you ask somebody, if you ask Michelle, 'Do we want to be involved in another war?' The answer is no. People are wary about it, understandably. They have seen the consequences of this last decade. They think in terms of blood and treasure it has not been worth it. It's not what they expected when they signed onto the Iraq War back in 2003.
"And so I recognize how important that debate is. And it's my belief that for — for me, the president — to act without consensus in a situation where there's not a direct imminent threat to the homeland or interest around the world.
But that's not the kind of precedent I want to set. I think it's important for me to listen, to engage in Congress, we're going to spend this week talking to members of Congress, answering their questions, and I'm going to speak to the American people tomorrow [Tuesday] night directly."