We fail at squashing radical Islam (or at least the worst of it) because we keep leaving doors open after we beat the old factions back. We go in, blow some shit up, shoot the people that shoot at us, make some kind of half-assed gesture towards rebuilding governments and state security forces, then leave and hope it all turns out ok. It never does.
Vetting refugees from Syria is already incredibly hard because there is so much chaos. Making the process more thorough is like giving an already drowned man a snorkel.
Because we are involved, and have been for so long, and things are getting way out of hand, we have a responsibility to those people. Not the jihadists, fawk those guys, but to those that have innocently been caught up in this mess. We already have sent billions in aid, so have others, and that's great, but the people have to go somewhere.
And yeah, it is a damned if you do, damned if you don't scenario. The odds of someone getting through that means to do harm is extremely low (there are easier, faster ways of getting supporters into the country), but there is always the risk that they will. Whatever happens, we need to do it with the right approach and attitude. The knee jerk reaction of "hell no they can't come here" is not leading with our best foot forward. Neither is Trumps "I'd bomb the shit out of them, I don't care", or "lets put them all in camps". He's trolling the GOP base so hard it's almost obscene.
We can't overcome this by giving the terrorists what they want, and that is to be afraid. Not only of them, but of anyone that comes from that region. They play a very specific game, and we have to be mindful of that. They can't hit us hard, or often, or repeatedly. All they can do is try to build their numbers over time and wear us down by making us chase them.
And to all those that proclaim "what about the children, or the vets, or the homeless, or etc", you can blow it out your pooper. Long after we're done with this current crisis, we're still going to have homeless kids and vets, and we'll pay the exact same amount of attention to them then as we do now, which is not enough. Don't make them suddenly important now that something else is on the radar.