Most just want assurances that we are not letting in ISIS sleeper agents with the refugees...
Put simply, I can frankly imagine no more onerous, slow, and difficult way of legally entering the United States than to pose as a Syrian refugee. When my wife (then fiancee) immigrated from Canada five years ago, she underwent far less scrutiny than a refugee would typically expect at the same time.
Considering the 2-year vetting process involved and subsequent surveillance, it's exceptionally unlikely that any competent terrorist would use the refugee system as a way of getting into the United States. Anyone attempting to do so would face a long slog through intense scrutiny by several agencies both within the United States and without, all of whom have the power to halt the refugee application at any time.
First, refugees from Syria and other countries have first had to register with the U.N. High Commissioner for Refugees. They would conduct interviews and background checks, take their biometric data, and establish whether they belong to one of roughly 45 "categories of concern" given their past lives and work history in their country of origin. That typically takes a year on its own.
Then the U.S. government begins its own vetting. The applicants are interviewed again, and their names and particulars are run through terrorism databases. Before they even make it onto US soil, they've undergone intense scrutiny by no fewer than four different federal agencies including the FBI, the USCIS, the DHS, and ICE. Once that's done, they have to go through yet another round of security screenings, including vetting through the Department of Defense, the State Department’s Consular Lookout and Support System, the FBI’s Terrorist Screening Center, the National Counterterrorism Center and others. This part of the process is classified, but it’s likely that they go through Intelligence Community reviews as well. At the same time, the refugees are given health screenings for diseases that could prevent them from relocating.
Now, assuming that they make it through all that, then they get to actually come to the United States, but their screening still isn't over. They undergo screening by the TSA and customs, and undergo training to learn basic information about the United States before they're moved to their permanent home.
But they're not done yet. Their status as a refugee expires in one year, and they need to apply for lawful permanent resident status. If they fail to do so, or their activities in the interim raise any concern, they are subject to immediate removal.
All in all, the time from beginning to end for a refugee to come to the United States is somewhere in the ballpark of 18 to 24 months before they get into the country, and another year after.
To hear many of the governors in the states, as well as media pundits say it, you'd swear that none of these safeguards were actually in place. Any terrorist who chose the refugee system for getting into the country could really only be described as incompetent. There are far faster, easier, and less risky (in terms of likelihood of getting caught) ways of getting into the states.