Because you’d rather have the President of the United States negotiate from strength than from weakness.
Most sentences containing the word “credibility” are nonsense. But the following, I submit, is not nonsense.
1. Threats are a tool of diplomacy.
2. The U.S. had reason to want the Assad gang not to use chemical weapons.
3. Barack Obama issued a threat: the use of chemical weapons would bring consequences in its train.
4. A party that makes threats and does not follow through when the announced trigger event happens is less convincing in making future threats. That’s a cost.
5. Therefore the fact that a threat was made constitutes an independent reason to carry it out. In that regard, a threat has much in common with a promise. You want your threats, like your promises, to be “credible”: i.e., worthy of belief.
6. The fact that backing down from a threat is costly is always an argument against making the threat in the first place. But it need not be a clinching argument.
7. Similarly, the fact that backing down is costly is always an argument for following through: again, clinching or not depending on other circumstances.
8. Ergo, you might want to back Obama’s play even if you thought that the immediate effects of an attack were likely to be, on balance, unfavorable rather than favorable. Or you might not.
The above is about actually making an attack on Syria. But there’s also a second-order question here. You and I and the Congress don’t get to decide about an attack. We get to decide whether to authorize the President to make an attack.* With that authorization in hand, he might be able to negotiate a better deal than he could without such an authorization in hand. So you could reasonably back Obama’s play even if you thought that an actual attack was a bad idea, in the hopes of getting the benefits of the authorization without an actual attack.
The fact that the Russians are now offering to take control of Syria’s chemical weapons might or might not be a head-fake. But I submit that it’s clearly the product of Obama’s threat to go to war. If a genuine offer is on the table, I hope that the Administration grabs it. But if the Russians and Syrians know that Obama can’t attack, that offer is likely to disappear.
And yes, as my dovish friends will no doubt remind me, I reasoned in just the same manner about authorizing GWB and his cronies to attack Iraq. And yes, we know now that they were never negotiating in good faith, being committed to war from the git-go. And yes, we now know that they were lying about the underlying facts. I have no reason to think that any such things are true about the current President or the people around him. Given a choice between believing Barack Obama and John Kerry on the one hand or believing Bashar al-Assad, Vladimir Putin, Rush Limbaugh, and Pam Geller on the other, I’m not likely to hesitate for very long.
For GWB and Cheney, war with Iraq looked like a huge partisan advantage, which is mostly what they cared about. Politically, I can see only risks and no gains for Obama in dropping bombs in Syria. So, if I were in the Congress, I would vote for an authorization to use force while hoping (and telling the President’s people I was hoping) that it would never need to be acted on.
Footnote If Obama manages to bluff the Syrians out of their chemical weapons, will we hear apologies from the critics on the left and right who have been talking about “amateur hour”?
Just asking.
Update Some of the commentary suggests that this sentence wasn’t clear. I did not intend to assert  that the President has the power to attack without authorization. (There’s apparently a controversy on this point, though I would have thought the War Powers Act made it clear that he didn’t, absent exigent circumstances.) I meant simply that the Congress cannot order the President to attack, even by declaring war.  The choice still remains in the President’s hands. This is unlike the situation when the Congress appropriates money, which the President is then obliged to spend.  So there’s no contradiction between voting to authorize force and hoping that force will not be used.
Second update And no, the fact that random positive reinforcement yields hard-to-break habits does not mean that sporadic punishment works better than consistent punishment. Reward and punishment are not symmetric, and bluffing is a bad habit in parents and diplomats alike.