When someone throws a drowning man a life preserver, he can’t afford to question his rescuer’s intentions.

Thus, this week President Obama eagerly grabbed a lifeline thrown by the Russians: a proposal that international monitors take control of and destroy Syria’s chemical arsenal. Moscow’s offer gave the president an excuse to postpone a congressional vote on authorizing a military strike against Syria — a strike meant to punish Bashar Assad for crossing a chemical-weapons “red line” by gassing civilians. The Kremlin saved Obama from public humiliation since he was almost certain to lose the vote.

Clearly Vladimir Putin, whose relationship with Obama is famously frosty, has no interest in doing him favors. Moscow’s gesture was meant to help its ally Assad by preventing a U.S. strike that could have benefited the Syrian opposition.

Yet this breather offers Obama one more chance to reshape an incoherent Syria policy — on Assad’s chemical weapons, and beyond.

On chemical arms, Obama must decide what he wants to make out of this new diplomatic opportunity.

Most experts doubt Assad will willingly turn over the bulk of these weapons, which will be difficult to find because he has now dispersed them, and even more difficult to destroy. Carrying out such a project in wartime could take months or years.

“We’re just going to have to see how serious the Russians are about telling the Syrians: ‘You have to do this,'” says Ryan Crocker, the veteran diplomat and former U.S. ambassador to Syria. “It will take an ‘or else.'” Even with pressure, collecting the huge stores of Syrian poison gas may be an impossible task.

Crocker, now dean of the Bush School of Government at Texas A&M, adds, “Most likely Putin and Assad are just playing for time, figuring the more time goes by, the less likely a strike.” Some Syria experts think Assad will try to play out the inspection game until 2014, when he wants to hold new presidential elections. Murhaf Jouejati, a Syria expert at National Defense University, says: “He’s going to cheat, lie, and ‘win’ the election, thumbing his nose at the world. Russia will help him.”

In other words, the new Syria diplomacy might well prove a sham.

To prevent this, the administration will have to insist on deadlines for any project to collect chemical arms. Obama’s team will need to use skilled behind-the-scenes diplomacy — not bluster and public denunciations — to rally broader support for a tough U.N. resolution that holds Assad accountable for crimes against his people. This should be the moment to isolate Assad — and the White House should make public the intercepts that prove his commanders ordered the strike.

Ironically, Iran could play a key role here. Iranian officials have a deep aversion to the use of poison gas, which Saddam Hussein used to kill tens of thousands of their countrymen during the Iran-Iraq war. Tweets and interviews from top Iranian officials have denounced the use of gas in Syria, without pointing a finger at the rebels (as Putin did). Some officials have openly held Assad responsible for the gas attacks.

While it still backs the Assad regime, Iran clearly wants to avoid another massacre by sarin. Behind-the-scenes contacts between Washington and Tehran, even indirect, might pave the way for a plausible project to control the bulk of his chemical weapons. That, in turn, could reduce the risk of such weapons falling into the hands of jihadi or other radical groups — something in which Moscow also shares an interest. (Rather than risk retaliation from Israel, Iran might even want to keep Syria from passing them on to Hezbollah.)

In other words, diplomacy over Assad’s chemical weapons might produce some useful results.

But, if the near-debacle over red lines proved anything, it’s that the White House needs a Syria strategy that goes beyond such immediate crises. Obama also needs to reconsider when and whether he would use force.

Russia wouldn’t have thrown out the idea of curbing Assad’s weapons without the threat of a potential U.S. strike — even though Secretary of State John Kerry insisted it would be “unbelievably small.”

Any further Syrian diplomacy will languish without such pressure behind it.

If Obama doesn’t want to use military strikes, he must revisit the issue of arming more moderate rebels. Otherwise Syria is headed for a division between a rump Assad state and so-called emirates run by well-armed radical Islamists who have squelched moderates with fewer weapons. Refugee flows will continue to flood Lebanon, Jordan, Turkey, and Iraq.

A narrow U.S. focus on chemical arms gives Assad carte blanche to slaughter his people by all other means possible. It virtually guarantees that Syria will implode in a way that threatens its neighbors.

Putin has (unwittingly) given Obama the chance to reconfigure a strategy that deals with the wider Syria problem. Time is short.