At least three dozen people in the United States suspected of ties to the Islamic State were under heavy electronic or physical surveillance even before the Paris attacks, senior American officials say. But unlike the attackers in France, the officials say, the majority of those under investigation here never traveled to Syria to fight alongside the Islamic State or receive training from it.

In many ways, the officials say, that makes the American investigations even harder. Those under investigation typically have little terrorism expertise or support from a cell, which makes thwarting an Islamic State-inspired attack in the United States less like stopping a traditional terrorist plot and more like trying to prevent a school shooting.

Stopping a potential attack has taken on new urgency after Paris, which served as a reminder that even people who have already caught the eye of intelligence services can spring attacks on short notice. Although at this point American officials say there is no credible threat from the Islamic State inside the United States, they worry that Paris could provide the spark to inspire angry, troubled people to finally do something violent, the New York Times reports.