With a congressional vote looming on the authorization of force against Syria, President Obama said Monday that a Russian proposal to avert a military strike represents a potential "breakthrough."

Earlier in the day, Russia proposed allowing Syria to turn over all of its chemical weapons as a compromise to prevent a U.S.-led strike — an idea first floated, seemingly off-the-cuff, by Secretary of State John Kerry. Syria reportedly agreed in theory to that proposal, forcing the U.S. to respond.

Speaking to CNN during one of six major TV interviews, Obama called the proposal a "potentially positive development" and said the administration would "run this to the ground."

"We have not seen these kinds of gestures up until now," Obama said. "The fact that the U.S. administration and I have said we are serious about this, I think has prompted some interesting conversations."

In an interview with PBS's Gwen Ifill, Obama reiterated his preference for a diplomatic as opposed to a military solution.

"If we can exhaust these diplomatic efforts and come up with a formula that gives the international community a verifiable, enforceable mechanism to deal with these chemical weapons in Syria, then I'm all for it," he said.

However, he added to NBC that he took the news of the proposal "with a grain of salt initially," saying he needed to ensure Russia and Syria could be trusted to comply with the proposed agreement.

As for the congressional vote, Obama said he was not "confident" he could win enough support among lawmakers for a strike.