The United States stands to:
1. Worsen global relations particularly with Russia and China.
2. Create more propaganda for Al Qaeda to use against us.
3. Help Al Qaeda create a new islamic extremist state in Syria. Al-Nusra, an arm of Al Qaeda spawned by Al Qaeda in Iraq has been said to be "the most aggressive and successful arm of the rebel force" and is a designated terrorist group by the UNITED STATES GOVERNMENT (so why is Obama asking us to help them?)
4. There is substantial evidence that the rebels may be using chemical weapons. In fact there is some dispute about whether Assad was using them at all. And if they are both using them we are hypocrites for fighting with the rebels against Assad.
5. There have been reports of the rebels persecuting Christians, even doing things like forcing Christians to convert at gunpoint. Many Christians have started leaving Syria, including Christians who lived there from long before.
What is in this for the United States and its interests? NOTHING. We can't even feel good about ourselves for getting involved because the rebels are up to the same sorts of atrocities and worse than what is accused of Assad.
No, it is not instrumental for the United States to go to war with Syria based on a cost-benefit analysis, because Syria cannot offer the United States anything from an economic perspective. Syria does not have a military base we want. Syria does not have oil reserves. A war would be costly, for little cost-benefit.