We announced last year that if Assad used chemical weapons it would be a game changer. Parenthetically, why we thought this was a "game changer" is still unclear. Assad was killing lots of people before using chemical weapons. Presumably the dead were unhappy with their murder even when it wasn't due to chemical weapons. See this poignant "comic." Then we caught Assad using chemical weapons to kill lots of people. Then we were stuck with defining "game changer," which we mulled over in public for a good bit, to no effect.
The arguments for using military force were that (1) we have to stop Assad from using chemical weapons and (2) we have to show the Iranians we mean business, because they keep trying to build a nuclear bomb. Assad had a front row seat as we wrecked Iraq and Afghanistan. Assad knows we can bomb him; he just didn't think we would. Turns out he was right.
I don't think throwing a few Cruise missiles into some dusty town-hall in Syria will convince Assad to stop bombing his own population. Neither will it convince Iran that we are ready to destroy them to keep them from building nukes. Bombing Syria would just kill a lot of poor people who don't have the wherewithal to get out of the way.
The lead up to Syria amounted to shouting through a bull-horn that we were about to throw a stick of dynamite into an out-house, the idea being that the neighbors will hear that you have dynamite and maybe quit playing Metallica at 3 a.m.
Problem is the neighbors already knew you had dynamite. They just don't believe you are going to blow up the outhouse, because you are going to get $h!# all over the place, most especially on yourself. Throwing dynamite into an out-house is a dumb idea. Not bombing Syria was the correct decision.
Making a lengthy public demonstration about bombing Syria was dumb. Being called on a bluff was unhelpful.
I do not think we lost credibility with the decision not to bomb. I don't think anyone took us too seriously to begin with. Our internal problems are news all over the world. For the last several years the president has not been able to get his own party in Congress to vote for his budgets, never mind Republicans, who so don't like his budget ideas they keep trying to shut the government down. Right now we cannot keep our government open, never mind take effective military action. We are not fooling anyone.