U.S. President Barack Obama, seeking to boost support for military action against Syria, said on Monday that Russia's offer to work with Damascus to put its chemical weapons under international control could be a breakthrough – if it is serious.

"This could potentially be a significant breakthrough," Obama told NBC News in an interview. "But we have to be skeptical because this is not how we've seen them operate over the last couple of years."  

Obama gave six television interviews on Monday, and was due to visit the Capitol on Tuesday to make his case to lawmakers from both parties before making a televised address from the White House in the evening. 

The president told CNN that any diplomatic effort to resolve the conflict in Syria must be serious.

"And we don't want just a stalling or delaying tactic to put off the pressure that we have ... right now," he said.

"We have to maintain this pressure, which is why I'll still be speaking to the nation tomorrow about why I think this is so important," he added.

The president said a breakthrough on control of Syrian chemical weapons would not solve "the underlying terrible conflict inside of Syria. But if we can accomplish this limited goal without taking military action, that would be my preference." 

In an interview with ABC News, Obama suggested that willingness on Syria's part to pursue a diplomatic solution could give Congress more time to decide on military action.

"I don't anticipate that you would see a succession of votes this week or anytime in the immediate future," Obama said. "So I think there will be time during the course of the debates here in the United States for the international community, the Russians and the Syrians to work with us and say is there a way to resolve this."

Speaking with NBC News, the president said he wasn't "confident" that Congress will vote to authorize military action in Syria. He further stated he has not decided whether to go forth with the strike if Congress votes against the plan. He will weigh the next step after the vote, he said.

Meanwhile, U.S. Senate Majority Leader Harry Reid abruptly backed off plans to schedule a test vote on Wednesday on a White House-backed resolution to authorize military strikes against Syria.

Just hours after saying he wanted the much-anticipated vote on Wednesday, Reid returned to the Senate to nix those plans. Aides said matters were fluid, particularly with Russia now trying to help find a way to avoid U.S. military force. They said a vote was still likely later in the week.

But two senior Republican U.S. senators, John McCain and Lindsey Graham, said on Monday the possibility of Assad giving up control of chemical weapons should make members of Congress more willing to vote for the authorization for the use of military force.

"Congress should proceed with its plans to consider and vote on the authorization for use of force that is now before the Senate, and today's development should make members of Congress more willing to vote yes," McCain and Graham said in a statement.

They said a yes vote would give Obama more leverage to press Russia and Syria to make good on a proposal to take chemical weapons out of Assad's hands.

But they also called on the Obama administration to immediately introduce a UN Security Council resolution spelling out "in clear, detailed terms" what the international community should expect from Assad's government.  

Clinton endorses Obama push

Former Secretary of State Hillary Clinton, a potential presidential candidate in 2016, waded into the debate, endorsing Obama's drive for Congress to approve military action.

She said the surrender of chemical weapons would be an "important step" but said such a proposal could only have come "in the context of a credible military threat by the United States."

Syria's Foreign Minister Walid al-Moualem "welcomed" the Russian proposal. Britain and France gave tentative support and UN Secretary General Ban Ki-moon said the Security Council should take up the issue.

The Russian offer came a few hours after Kerry had suggested in London, in response to a reporter's question, that Syrian President Bashar Assad could avoid a military strike by surrendering his chemical arsenal.

A senior U.S. official described Kerry's comment as rhetorical, but said Kerry told Russian Foreign Minister Sergei Lavrov in a later phone call that while he was skeptical about the prospect he would examine any serious proposal.