"The president has, I think, made up a law that we never passed," said Sen. Russell Feingold, D-Wis.
Sen. Arlen Specter, R-Penn., chairman of the Senate Judiciary Committee, said he intends to hold hearings.
"They talk about constitutional authority," Specter said. "There are limits as to what the president can do."
Senate Democratic Leader Harry Reid of Nevada also called for an investigation, and House Democratic leaders asked Speaker Dennis Hastert to create a bipartisan panel to do the same.
President Bush acknowledged Saturday that since October 2001 he has authorized the National Security Agency to eavesdrop on international phone calls and e-mails of people within the United States without seeking warrants from courts.
The New York Times disclosed the existence of the program last week. Bush and other administration officials initially refused to discuss the surveillance or their legal authority, citing security concerns.
CBS News correspondent Bill Plante reports Mr. Bush lashed out at news organizations for making the story public. Mr. Bush said the report relied on unauthorized disclosure of classified information that "damages our national security and puts our citizens at risk." Disclosure of the program helped generate opposition to a renewal of the Patriot Act in the Senate on Friday.
"The activities I have authorized make it more likely that killers like these 9/11 hijackers will be identified and located in time," Mr. Bush said in a rare live address. "And the activities conducted under this authorization have helped detect and prevent possible terrorist attacks in the United States and abroad."
He said congressional leaders have been apprised of the secret order "more than a dozen times."
President Bush took personal responsibility for the war in Iraq Sunday evening,, where in March 2003, he announced the U.S.-led invasion. Nearly three years later, more than 2,150 U.S. soldiers have died, Bush's popularity has plummeted and about half of Americans think the war was a mistake. Yet a strong majority opposes an immediate withdrawal of U.S. forces.
The address came on the heels of four major speeches in which President Bush acknowledged setbacks and surprises in the war and took responsibility for ordering the invasion on the basis of inaccurate intelligence. The admissions were part of a White House effort to address complaints that Mr. Bush lacked a solid strategy for the war and has been oblivious to the violence that Americans plainly see on television.
"I know that some of my decisions have led to terrible loss and not one of those decisions has been taken lightly," he said. "I know that this war is controversial, yet being your president requires doing what I believe is right and accepting the consequences."
First Amendment legal expert Floyd Abrams told CBS News correspondent Randall Pinkston the president is attempting to mitigate his sidestepping of Congress by saying he had informed some lawmakers.
"It is mitigated in the sense that Congress was not completely uninformed," Abrams said. "As a legal matter though, what the president has authorized 30 times may have been illegal 30 times."
"It's been briefed to the Congress over a dozen times, and, in fact, it is a program that is, by every effort we've been able to make, consistent with the statutes and with the law," Vice President Dick Cheney said Sunday in a televised interview to be broadcast Monday evening: "It's the kind of capability if we'd had before 9/11 might have led us to be able to prevent 9/11."
President Bush and other administration officials also have said congressional leaders were briefed regularly on the program. Sen. John McCain, R-Ariz., said there were no objections raised by lawmakers who were told about it.