The United States participates in a mutual Visa Waiver Program with 38 countries. This allows US citizens to travel to those countries without a visa, and vice versa.
Visa Waiver Program | Homeland Security
The 38 countries are Andorra, Australia, Austria, Belgium, Brunei, Chile, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hong Kong, Hungary, Iceland, Ireland, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malaysia, Malta, Monaco, Nauru, Netherlands, New Zealand, Norway, Papua New Guinea, Portugal, San Marino, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland, Taiwan, and the United Kingdom.
Obama removed Iraq, Syria, Iran, and Sudan from the Visa Waiver Program. Anyone traveling to the US from those countries is required to get a visa, along with the other 154 countries not in the Visa Waiver Program.
The reason the terrorists have had such successes in Europe is because Europe is a multiple of nations with varying levels of control over the movements of their populations. Their borders are basically wide open.
Three of the terrorists who would later carry out the Paris attacks were able to cross over the Austrian-Hungarian border without being caught, even though all were known extremists, and one was wanted on a terrorism warrant while another was on an EU watch list, because that border station was not tapped into either list.
Since we are one nation, all US border control points are tapped into the watch lists. The US also uses Passenger Name Records (PNR). This is travel information collected and collated by every airline for every passenger who travels in, out, and around the US. It is a crucial method by which our police state tracks our movements.
Believe it or not, Europe is more hyped about protecting the privacy of its citizens than the US. Because Hitler. No, really. Because Hitler. So they don't have PNRs. But their thinking on this is changing due to the Paris and Brussels attacks.
So the European continent is a wide open playing field for terrorists. They can move about completely undetected, and they know this.
Thus, US intelligence is a casting a wary eye at the Visa Waiver Program. If terrorists can easily penetrate Europe using fake papers, the Visa Waiver Program is one more lowered barrier to jumping here.