It seems to me that there is a relatively simple solution to this problem if neither side insists on complete victory:
First of all it is foolish to assert that we can effectively vet 10,000 Syrian refugees when numerous security officials and experts (including the director of the FBI) say it isn't so. All 10,000 of them can be interviewed for 24 hours straight, but without an existing database of detailed information on these people, an expert liar with only the most basic of ID documents will make it through the process. Such a database doesn't exist.
Secondly, over 99% of the refugees can be law abiding, decent people but if the remainder are terrorists we have a serious problem. Gun control advocates (many of who are advocating taking in more than 10,000 refugees) like to argue that if one person's life is saved by greater restrictions on guns, then they are worth it. I would think, therefore, that they would be very open to the argument that if only one person dies because of allowing these refugees into our country, then it won't be worth it.
However there is a solution that will enable us to provide significant support and assistance to the people who have suffered terribly at the hands of the twin monsters Assad and ISIS, and with a very low risk of importing terrorists who will visit suffering on our citizens.
Unfortunately the conflicts in Syria have, undoubtedly, resulted in the deaths of many male heads of families. We can be sure the number exceeds 10,000. The solution to the problem is to offer asylum only to widows and their children. Certainly there are least 10,000 Syrians who would qualify under this condition and if implemented I would even argue that we could increase the number of refugees we accept by as much as 10 fold that number.
Clearly, widows and their children are the most vulnerable of the Syrian refugees and the ones most in need of our help. Yes, young (or old) single males are at risk in Syria but they are also the most likely Syrians to be terrorists attempting to enter our country. We don't owe the refugees a process that is blind to age or gender. We don't owe them anything.
I believe we should be helping these people who have suffered so much. If the West, and most importantly the US, had intervened early on, there might not now be a refugee crisis, but our need to help these people has nothing to do with real or imagined culpability for their predicament. We need to help them because it is the right thing to do. However it is not the right thing to do if it can't be done without minimizing the risks to Americans.
Arguing that there is no risk or that is too small to even consider is nonsense and no one making it will be happy to have the blood of innocents on their hands if they are proven wrong. In fact, I can imagine the back pedaling now..."Well of course there was a risk if we weren't going to vet them properly," or "There was no risk at the time but our continued aggression in the region drove some of these people into the arms of the terrorists." It doesn't matter though. We can meet our humanitarian obligation without assuming an appreciable risk.
Insisting that young single men be part of the accepted refugee population will be seen as precisely what it is: An insistence on getting one's way, regardless of consequences.
Any arguments for why this proposed solution cannot or will not work or why it should be adopted are welcome.