I don't doubt we would win, but there would be a huge death toll on both sides.
The US wanted to go after Iran for a good while now. Go after Syria, and Iran will come in. The Russians and Iran are allies, and Russia and China already warned the US not to invade Iran. Now they are telling the US not to attack Syria.
If the US pisses off China, China will pull on the US debt, and the US economy will experience market prices going through the roof while the USD falls way down in value.
If the shit hit the fan, it will go long and hard, in the end the US will push for a financial reset. At that time, RFID chips will become standard, and all currency will be digital.