No one has the RIGHT to enter the US. If the American People, as a whole, say "No Syrian Refugees", then that's what public policy ought to be, unless there is some super-compelling reason that is in the best interest of the American People (citizens) to take them in.
We don't have to allow ANY immigrants. What's good for immigrants may not be good for the American Citizenry. And the American Citizenry is SUPPOSED to come first.
Humans, regardless of the superficial differences attributable to the random chance of where one was born, to what race one belongs, or to what deity (or lack thereof) one prays, come first. Period. When America, a land of relative wealth and stability, has the capacity to aid and assist our fellow man in need, but refuses, then the moral judgment of all civilized people should be that of condemnation. Any objection or protestation to the contrary betrays the moral foundations of our modern society, to which maybe you do not wish to belong, but many, if not most, of us do. Petty nationalism, such as that demonstrated in your post, is abhorrent and, thankfully, being gradually tossed aside by an emergent group of Americans who view all humans as interconnected, interdependent, and ethically bound to help one another without regard to something as arbitrary as imaginary lines on a map.