The head of the National Security Agency said recruiting so-called cyberwarriors hasn’t been difficult despite the recent disclosures of classified surveillance programs by a former government contractor.

The agency has received tens of thousands of applications for just a couple of thousand job openings, according to Army Gen. Keith Alexander, who oversees both the agency and U.S. Cyber Command at Fort Meade, Md. He didn’t specify a time period.

“Actually, on the NSA side, which can influence onto the Cyber Command side, we’ve had a lot of applicants — around 20,000 to 40,000 for 2,000 jobs,” he said last week during a cybersecurity conference in Washington, D.C. “It’s amazing.”

His comments seemed to undercut those made by other panelists who suggested the political gridlock on Capitol Hill, D.C., is discouraging potential candidates from seeking the highly technical government jobs. The government shutdown, now in its 14th day, began Oct. 1 after Congress failed to pass a budget or short-term funding resolution for fiscal 2014.

While Alexander said the shutdown is “making it hard” for some employees to continue working in government, he also described cybersecurity work as a “tremendous opportunity” for young people entering the military services.

“This generation is coming up cyber savvy,” he said, after explaining how his almost 2-year-old granddaughter knows how to use an iPad to watch movies on Netflix. “We can train them. We can educate them.”

The Defense Department wants to boost spending on “cyberspace operations” 21 percent to $4.7 billion in fiscal 2014.

U.S. Cyber Command alone plans to dramatically increase the number of personnel to 4,900 by 2015 from 900 today. In coming years, it expects to build a new joint operations center at Fort Meade and boost the ranks of military and civilian personnel assigned to cyberwarfare teams in Maryland, Texas, Georgia and Hawaii.

At the National Security Agency, both technical and non-technical jobs are in demand, Alexander said. An opening for a “civil liberties and privacy officer” drew several dozen resumes, he said.

“We have the technical foundation and the academic acumen at NSA to help build the knowledge set for these people,” Alexander said. “I don’t see an issue there and I’m not getting it from the services that that’s yet an issue in hiring.”

He did, however, say that disclosures of surveillance programs have probably doomed, at least temporarily, legislation designed to make it easier for the government to share information about threats with the private sector.

Edward Snowden, a former employee of McLean, Va.-based Booz Allen Hamilton Inc. who worked as a contractor for the NSA, is wanted for leaking information to the media about classified programs to collect personal user data from telephone and Internet companies. Snowden received temporary asylum in Russia after fleeing the U.S.

The leaks have continued. The Washington Post on Monday reported that the National Security Agency is collecting hundreds of millions of contact lists from personal e-mail and instant messaging accounts.

Alexander criticized news accounts of the programs that he said have “greatly sensationalized and inflamed” the facts. He also seemed to indicate he supports Snowden’s arrest.

“Shutdown Snowden? I’m with you,” he quipped in response to a question that referenced both the government shutdown and the former contractor.

The House of Representatives on April 18 passed the Cyber Intelligence Sharing and Protection Act. The bill, H.R. 624, was sponsored by Rep. Mike Rogers, R-Mich., chairman of the House Intelligence Committee, and co-sponsored by Rep. C.A. “Dutch” Ruppersberger, D-Md., the panel’s ranking member.

The legislation would allow agencies such as the Defense Department and National Security Agency to share anonymous information about cyber threats with the private sector, and vice versa. Like government agencies, companies from Google Inc. to Lockheed Martin Corp., the world’s largest defense contractor, have been targeted in computer attacks traced to groups in China and other countries.

Lockheed and L-3 Communications Holdings Inc. in 2011 had their networks disrupted after hackers gained codes to authenticating devices called RSA SecurID made by EMC Corp. (The tokens are also used by Military.com’s parent company, Monster Worldwide Inc.).

A Chinese espionage group since 2006 has stolen hundreds of terabytes of information from at least 141 companies across 20 major industries, including aerospace and defense, according to a February report from Mandiant, a closely held company based in Alexandria that sells information-security services.

Cyber theft is estimated to cost as much as $400 billion in economic losses a year and “many of the same vulnerabilities used to steal trade secrets can be used to attack the critical infrastructure we depend on every day,” according to a background briefing on the legislation.

The revelations of the surveillance programs, though, have made corporate executives concerned that closer collaboration with the government will alienate their customers, making the politics of the bill temporarily impossible.

Even Alexander seemed to acknowledge as much.

“The trust factor has to be built back because, right now, the way the Snowden thing has been sensationalized and inflamed makes it sound like we’re listening to all phone calls and we’re reading everybody’s e-mails,” he said. “That is factually incorrect. One, it would be impossible and two, it would be illegal.”