A common view on the left is this: a moral responsibility falls on western countries to accept refugees, first because of the scale and severity of the humanitarian crisis brought on by the Syrian Civil War, and also because they have the capacity to do something about it. There is also a stronger view that western countries in particular are responsible for accepting refugees because of their involvement in the Iraq War, i.e., because they produced the conditions that led to Syrian Civil War and ISIS in the first place. Someone who believes that might think that America's response to the crisis is especially egregious compared to other countries, given that it has accepted only 10,000 refugees in the past year (very little compared to other countries), despite being the architect of the invasion of Iraq.
Frequently, people more firmly on the left don't think of the refugee problem and terrorism as related issues. The argument might go something like this: because it's "racist" or "Islamophobic" to assert that Muslims are any more likely to be terrorists than anyone else, the idea that accepting refugees is a security issue at all is merely the result of prejudice. A less extreme view argues that America has so many counter-terrorism and intelligence resources that it is very well equipped to identify the statistically insignificant number of refugees who may take advantage of their residence in the United States and commit terrorist acts, and to prevent them from entering the country (some might even argue that America is better equipped than the European countries that have been more generous towards refugees).
Now, to respond to the question more directly. Islamic terrorism in the Americas and in Europe are both domestic and international. Many -- but not all -- of those who commit acts of terror in western countries are natural born or naturalized citizens of those countries, who live in them and prepare attacks in them. Thus, Islamic terrorism is domestic in the sense that counter-terrorism measures that might prevent these attacks frequently involve surveillance of people who live "here". But it's also international in the sense that terrorists typically affiliate themselves with international terrorist organizations, ideologies and movements, and those organizations frequently claim such attacks as their own, even if they often don't provide operational support or guidance to the agents of the attacks. (And we're leaving aside that I'm conflating the more broad "terrorism" here with "Islamic terrorism".)
Undoubtedly, Europe's policy towards refugees and its porous borders increase the capacity of terrorist organizations to carry out attacks on European countries is a highly politicized. Concerns of those on the right aren't entirely baseless: recall that some among those involved in the Paris attacks last November used a stolen Syrian passport to pose as a refugee (
http://www.nytimes.com/2015/11/16/world/europe/paris-attacks-shift-europes-migrant-focus-to-security.html?_r=0), and that the perpetuators of Boston Marathon bombing had received asylum to live in the US (
https://www.washingtonpost.com/politics/details-emerge-on-suspected-boston-bombers/2013/04/19/ef2c2566-a8e4-11e2-a8e2-5b98cb59187f_story.html). But, as is typical in American politics, political discussions on this issue, have nothing to do with policy. Rather, it's just another culture war: that is, it's ultimately based on defending and attacking premises, which are unfalsifiable and cannot be definitively justified empirically, and allegiance to which forms a basis of one's political identity. In this instance, the central belief is whether or not refugees are good people or not, and, as a corollary, whether or not Islam is morally corrupting.
I am the Stig
