The White House asked The New York Times not to publish this article, arguing that it could jeopardize continuing investigations and alert would-be terrorists that they might be under scrutiny. After meeting with senior administration officials to hear their concerns, the newspaper delayed publication for a year to conduct additional reporting. Some information that administration officials argued could be useful to terrorists has been omitted. While many details about the program remain secret, officials familiar with it said the N.S.A. eavesdropped without warrants on up to 500 people in the United States at any given time.