At a civic breakfast in Manhattan, the third term senior senator from New York said Obama "had just the right tone" in his address late Sunday and rightly praised predecessor George Bush.
While "al-Qaida is much, much weaker" and "can't communicate electronically . . . that doesn't mean there aren't individuals like the Times Square bomber who might decide to do things on their own," Schumer said.
But federal agencies have not detected upgrades in terror activity or reported terrorist attempts, he said he was told by FBI and Homeland Security officials.
He cited improvements in U.S. security measures. "We are so good now at monitoring all the electronic conversations the terrorists have. Is it foolproof? No.
"But it's not an accident that New York and America have not been attacked since 9/11. We'll have to be vigilant, obviously."
Schumer spoke of some closure for family members chagrined for years that bin Laden could survive the murder of those loved ones.
He called bin Laden's death a turning point in the war on terror "like Saratoga or Gettysburg."