The likelihood of being killed by a terrorist attack from a refugee in the United States has been calculated at 1 in 3.6 billion.
I think there are three problems here, and this is the second article I've seen these same three problems show up in, so I'd like to address it.
First, there is no real opposition to "refugees," but rather "Muslim refugees from nations with Muslim terror problems." In fact, among Americans who oppose taking in more Muslim refugees, I suspect there would be a strong willingness to take in Christian and Yazidi refugees from these same regions. The conflation of terms here implies a general xenophobia rather than specific concerns about a specific population, and although I don't think it is intentional, it is insulting.
Second, limiting the geographical area to the United States is also problematic because most of the Muslim refugees from nations with Muslim terror problems have gone to other places, such as Europe. So, to be relevant, one should include all nations that have accepted these refugees.
Third, the fear of taking large numbers of these particular refugees is not limited to terrorism. When Europe began taking in large numbers of these refugees, there were immediate problems with sexual assault and other crimes.
Because of these factors, it seems to me that the only really meaningful statistic would cover the particular refugee populations in question regardless of geographic area of resettlement and it would include all crimes, not just terrorism. If that statistic were used, I suspect the argument would look very different.
All that said, I have yet to see anyone arguing for bringing in 100,000 Muslim refugees from nations with Muslim terror problems address some of the deeper concerns of their opponents, including issues of long-term assimilation and the radicalization of second and third generation Muslims in Western nations. These are also important issues, and if someone wanted to change my mind about bringing in tens of thousands of Muslim refugees from nations with Muslim terror problems, they would have to address them as well.