This would apply to Christian Syrians, not Islamic Syrians. They may be leaving due to unrest but that does not make them a refugee.
Refugee also includes, in special circumstances the President after appropriate consultation may specify, any person who is within the country of such person's nationality or, in the case of a person having no nationality, within the country in which such person is habitually residing, and who is persecuted or who has a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion.
The term "appropriate consultation" means, with respect to the admission of refugees and allocation of refugee admissions, discussions in person by designated Cabinet-level representatives of the President with members of the Committees on the Judiciary of the Senate and of the House of Representatives to review the refugee situation or emergency refugee situation, to project the extent of possible participation of the United States therein, to discuss the reasons for believing that the proposed admission of refugees is justified by humanitarian concerns or grave humanitarian concerns or is otherwise in the national interest, and to provide such members with the following information:
To the extent possible, information described in this subsection shall be provided at least two weeks in advance of discussions in person by designated representatives of the President with such members.
Has "appropriate consultation" occurred? Have discussions in person by designated Cabinet-level representatives of the President with members of the Committees on the Judiciary of the Senate and of the House of Representatives occurred?
8 USC § 1101(a)(42), 8 USC § 1157(e), 8 USC § 1185(b)(1)(B)(i)
We have no law that demands we take anyone into this country - for any reason!
We already have too many illerate, poverty stricken aliens who do NOT speak English and need welfare, free medical treatment, untreated infectious diseases and don't necessarily agree with our form of government and probably do not wish us well!