The revelations have renewed debate over surveillance in the United States and overseas in the name of fighting terrorism, with supporters saying the programs revealed by Snowden are legal and have helped stop terror plots. Civil liberties advocates, however, call the measures dangerous and unacceptable intrusions.
Such criticisms have put Obama and his allies on the issue -- both Democrats and Republicans -- on the defensive against mounting criticisms from a similarly bipartisan group of critics demanding changes to rein in the programs.
There also is a sharp division among Americans over the issue.
A Gallup poll released Wednesday found that 44% of Americans believe Snowden did the right thing by releasing details about the classified surveillance programs, while 42% said it was wrong and 14% said they were unsure.
The poll for that question had a 6% margin of error.
It also found that more Americans disapprove than approve of the government's surveillance programs, 53% to 37%. Ten percent had no opinion.
The poll for that question had a 4% margin of error.
Those differences were on display Wednesday when Alexander, the director of the National Security Agency, testified at a hearing into cybersecurity technology and civil liberties.
Officials have been unable to explain controversial data mining programs because they have been classified, Alexander testified.
But Alexander rejected the Snowden's claim that the NSA could tap into any American's phone or computer.
"I know of no way to do that," Alexander said.
But he testified that phone records obtained by the government helped prevent "dozens" of terrorist events.
He would not discuss disrupted plots broadly, saying they were classified. But he did say federal data mining appeared to play a role in helping to disrupt a plot in recent years to attack the New York subway system.
Alexander said information developed overseas was passed along to the FBI, which he said was able to identify eventual suspect Najibullah Zazi in Colorado and ultimately uncover a plot. Zazi pleaded guilty to terror-related charges in 2010.
While not on the roster for Wednesday's hearing, another administration official in the spotlight is Director of National Intelligence James Clapper, whom Democratic Sen. Ron Wyden has singled out for how he answered questions about the telephone surveillance program in March.
In March, Wyden asked Clapper whether the NSA collects "any type of data at all on millions or hundreds of millions of Americans?"
"No sir," Clapper said.
On Saturday, Clapper told NBC News that he answered in the "most truthful or least most untruthful manner" possible.
Clapper told NBC that he had interpreted "collection" to mean actually examining the materials gathered by the NSA.
He previously told the National Journal he had meant that "the NSA does not voyeuristically pore through U.S. citizens' e-mails," but he did not mention e-mails at the hearing.
Fallout over revelations about the NSA's intelligence-gathering has reached the European Union's governing body, where Vice President Viviane Reding raised concerns that the United States may have targeted some of its citizens.
Reding said she plans to raise the issue during a meeting Friday with U.S. Attorney General Eric Holder.
"The respect for fundamental rights and the rule of law are the foundations of the EU-U.S. relationship. This common understanding has been, and must remain, the basis of cooperation between us in the area of Justice," Reding, the EU commissioner for justice, said Wednesday.
"Trust that the rule of law will be respected is also essential to the stability and growth of the digital economy, including transatlantic business. This is of paramount importance for individuals and companies alike."