#1, refugees receive very modest aid. In general, government agencies provide income relief for 6 months, and, after that, the refugees are on their own.
#2, there is an onerous refugee vetting process for those entering the US. This is not a matter of the first 10,000 people to reach the ticket window. Refugees in camps in Jordan, Turkey, Lebanon and elsewhere begin application processes which take years, with preferences given to specific categories, such as those who have relatives in the USA or those who have helped US companies or military units, etc. In fact, the process is so long that my guess is that most of the 10,000 who enter the United States would have initiated their applications prior to the rise of ISIS.
#3, as of now, there is some evidence that 1 of the 7 (8?) attackers recently entered Europe along with the refugees. In my mind, even if that is proven, it would not be a good excuse to deny asylum to the hundreds of thousands in need.
Europe does have a vetting problem now because it has no system and there’s not an ocean separating Europe from western Asia. But that’s not a problem for the US.