While there can be no doubt whatsoever that a humane United States of America would take gladly take in tens of thousands of refugees from the war torn state of Syria, it is important to keep in mind that we need to be prepared for them too.
A meticulously prepared process needs to be formed to transport refugees across the Atlantic, house them, feed them, educate them, etc. If this is not done properly, then it will be difficult to ensure safe lives for these long-suffering people.
This is far from an impossible task. The post-WWII influx of GIs was dealt with very successfully. Vast numbers of soldiers were safely transported back to their country, and were given places to live by the usage of tract housing and low-cost Lustron houses.
There is no barrier to helping a fellow human.