On Thursday, Representative Howard P. McKeon of California, the Republican chairman of the House Armed Services Committee, sent a similar letter to Mr. Obama stressing that the country was about to reach the War Powers Resolution deadline, which he portrayed as a “critical juncture.”

And on Friday, the American Civil Liberties Union also wrote to Mr. Obama expressing its “profound concern” that he was about to violate the War Powers Resolution, and arguing that he had no legal authority to use military force in Libya.

Administration officials offered no theory for why continuing the air war in Libya in the absence of Congressional authorization and beyond the deadline would be lawful. Jack Goldsmith, a Harvard law professor who led the Justice Department’s Office of Legal Counsel in 2003 and 2004, portrayed it as a significant constitutional moment.

“There may be facts of which we are unaware, but this appears to be the first time that any president has violated the War Powers Resolution’s requirement either to terminate the use of armed forces within 60 days after the initiation of hostilities or get Congress’s support,” Mr. Goldsmith said.

Jay Carney, the White House press secretary, said that the validity of the War Powers Resolution had been so debated that writings about it “over the years could fill this room, and none of it would be conclusive.”

Congress enacted the resolution in 1973, overriding President Richard M. Nixon’s veto, in an effort to reassert its constitutional role in making decisions about whether the country would get involved in significant armed conflicts.

Several parts of the resolution have been repeatedly challenged by presidents. But a 1980 opinion by the Justice Department’s Office of Legal Counsel concluded that the 60-day limit was constitutional. (The law allows presidents to extend the deadline by 30 days if necessary to protect the safety of forces as they withdraw, which does not appear to apply to an air campaign.)