No longer facing the imminent threat of a U.S. military strike, the Assad regime is dragging its feet on relinquishing its chemical weapons -- leaving U.S. officials scrambling to pressure the Syrian government to honor the terms of last year's deal.

The Obama administration acknowledged on Thursday that the regime has shipped out less than 5 percent of its chemical arms. The country is weeks behind schedule, and may miss next week's deadline to ship all its chemical agents out of the country.

This, despite President Obama declaring in his State of the Union address that Syria's chemical weapons "are being eliminated" thanks to American diplomacy.

The administration still hopes diplomacy will prevail. It also may have few other options, with little appetite in Congress for military intervention.

White House Press Secretary Jay Carney said Friday that officials are working with partners to "keep up the pressure" on the regime.

"They have an obligation here. They have committed to doing this," Carney said.

State Department spokeswoman Jen Psaki said Secretary of State John Kerry spoke with his Russian counterpart earlier in the week about the concerns, and asked for Moscow's help.

"This is not rocket science here. They're dragging their feet," she said. "We need them to pick up those feet and run with this and move forward in moving the chemical weapons stockpile to the port."

Assad sidelined talk of a military strike last September, when he publicly agreed to give up his chemical weapons.

Asked if military force is still an option, Psaki said "you never take a tool off the table."

But since the administration threatened military force last year following evidence that the Assad regime crossed the "red line" and used chemical weapons, momentum behind a possible strike has flagged.

In September, an Associated Press poll found most Americans oppose a military strike in Syria. And Obama included this passage in his State of the Union: "As Commander-in-Chief, I have used force when needed to protect the American people, and I will never hesitate to do so as long as I hold this office. But I will not send our troops into harm's way unless it's truly necessary; nor will I allow our sons and daughters to be mired in open-ended conflicts."

Some question whether Russia can be counted on to accelerate Syria's cooperation now. Sen. Lindsey Graham, R-S.C., told Reuters: "Having the Russians disarm Assad is sort of like Mussolini disarming Hitler; I'm not so sure it's going to work."

The situation in Syria is no less volatile than it was when the deal was announced, with Assad refusing to leave power and terror groups taking root in the country amid the fighting.

Earlier this week, Director of National Intelligence James Clapper warned in a written report to the Senate intelligence committee that the chemical weapons deal, and Russian support, have helped give the Assad regime "legitimacy."

He also said 7,000 foreign fighters are now operating in Syria, noting his concern that Al Qaeda could use Syria to launch a terror attack against the U.S.

Meanwhile, U.S. vessel the MV Cape Ray, which was configured to neutralize Syria's chemical agents, left Norfolk on Monday and is expected in Rota, Spain, next week. It's the first time ever that countries have attempted to destroy mustard, sarin, and vx nerve gas at sea.

But U.S. Defense officials say none of Syria's chemical stockpiles have yet arrived at the port in Italy where the MV Cape Ray is slated to begin its mission, because Bashar Assad is still holding roughly 96 percent of his stockpile.

Fox News' Jennifer Griffin contributed to this report.