Syrian refugees entering the country bring a burden on issues outside of security. Recently, it was estimated that it costs $20k to settle the refugees. This ties into the false cries of globalism; those $20k would have been much better spent on a wounded homeless veteran. And that's not even including all the bad that can happen from it.
Some may argue that stopping undocumented immigration is a harsh or unfair action, but it is a proven hole in the defense of the U.S. If it is allowing attackers to come in from other countries under the radar, then it should be stopped. These vulnerabilities in the nation's security should not be overlooked.
Undocumented immigration is not the reason for terrorism. The reason for terrorism is hate and ignorance. There are plenty of attacks that happen all over the world that are committed by natural born citizens. Look at Dylan Roof, who killed a bunch of people in a church. He is just a white boy who is a citizen of the US. How about the OK City bombing? Timothy McVeigh was a white natural born citizen. We can't blame immigrants for every violent act, and we can't pretend that they are any more of a threat than our neighbors.
I agree illegal immigration is a problem, but I think much could be done to fix that problem by making it easier for good, educated people to get in here legally without having to wait for years. If good people could get in easily legally then the only people coming in illegally would be the bad ones, and waging war against illegals would be much more satisfying then kicking out innocent people who are just trying to survive here because their own countries are bad.
A country with land borders will always have problems with undocumented immigrants, because there is no way to police 100% of a border. Making a society which is welcoming to immigrants and prevents them from being marginalised is the only way to stop these kinds of attacks. The "Us and Them" has to stop.