Then there are the liberals. Oh, for the love of god can you all please stop moralizing everything? (Know how much you liberals love it when conservatives moralize their pet issues? Yeah, think of how open that makes you to their viewpoint.) There are very good logical reasons to support taking in refugees. Yes, it still may be a very noble thing to do and all that. David Bier of the libertarian thinktank the Foundation for Economic Education outlines 6 reasons to welcome refugees, and five of them are non-moralizing reasons: (1) The Paris attackers were not refugees; (2) US refugees don’t become terrorists (some people cite the Tsarnaevs as refugees, but they only got secondary refugee status from their parents being refugees, were 8 and 15 when they arrived, and the "flags" that they had associated with extremists came in 2011 - after they came here); (4) ISIS sees Syrian refugees as traitors; (5) Turning away allies will make us less safe.
Turning away refugees may actually increase the likelihood that someone coming from Syria is a terrorist. In fact, accepting more of all immigrants makes us more safe. Take, for example, organ donations. Some argue that there should be an open market for organs. People would pay for organs, the supply would increase, and waiting lists would shrink. But, think now about who is most likely to sell an organ if a substantial sum of cash could be made from it. People who need money the most and who least value their own bodies. Drug users, homeless people prostitutes, and other people who are at high risk for diseases like hepatitis, HIV, and other things we don't want infecting organs. Since no test is perfect, a cash market would increase the number of diseased organs transplanted to already-sick recipients. A donor "market" partially resolves this adverse selection problem by pre-screening the most desperate from supplying their organs. The lack of payment becomes a disincentive for participating.
The immigration-security problem is sort of like this, but in reverse. If we raise the cost of immigrating to the US, we de facto limit the ability of the poor and marginalized to be able to participate. Moreover, we turn the screening process over to smugglers, who are likely to be much less particular about who pays them to get into the US. Cutting off access to immigration for everyone almost guarantees that Syrians who do come to the US will try to do so by subverting the legal process, making it less likely that we will be able to thwart future attacks.
(A similar argument, by the way, could be made for lowering voting restrictions instead of tightening them.)