Now, I am not saying this situation is remotely like that one; Assad is not likely to Pearl Harbor us even if he wants to (though one could argue his dad did via Hezbollah in '83,) and we ARE likely to have plenty of time and warning before he gains that ability. The point is we live in a republic rather than democracy precisely because the majority is not always right (something the German electorate underscored differently shortly before 1940.) Just because the majority do/not want something does not mean the country should/not do it. American majorities have supported slavery, prohibition and more than a few ill-advised military campaigns. That did not make any of them moral or wise, and many things that were both did not suddenly cease to be either when public support vanished.
Assad is not invading anybody, he is fighting a civil war in his country. If our government knows something we don't and wants to help overthrow him then they should use the institutions built to do such things such as the CIA and possibly some Special Forces to help train those we want to support. The government can consider arming them through back channels if they feel it is that important. But, the mission of our military is to uphold our constitution and defend our nation (and to help those we have entered treaties with promising support if they are attacked). Syria has not attacked us, they have not attacked our treaty allies and they are not violating out constitution.
You can yap about Republican forms of government versus a pure democracy where the majority rules no matter how slim the majority, but the fact is that every polling shows very clearly how one sided an affair this is. The nation of the United States of America does not support bombing Syria, it is not even close. Period. Regardless of political party or persuasion.
-Brandon Sanderson, The Way of Kings