To help find an answer, Hayden turned to Carly Fiorina, former CEO of Hewlett-Packard, whom he had selected to chair the CIA's External Advisory Board. She responded with a warning that the agency would have to adapt to confront rapidly-changing public expectations.
"She contributed a great deal," Hayden recalled, noting that the meetings were classified. "It confirmed for me what I thought was a coming crisis. It helped me with my judgment."
Fiorina, who on Monday announced a bid for the Republican presidential nomination, has never held elected office or served in a Cabinet position. She is known mostly for her work in the tech industry -- serving as Hewlett-Packard's CEO from 1999 until her unceremonious ousting in 2005 -- and for an unsuccessful bid for Senate in California in 2010.
But in the months leading up to her White House announcement, Fiorina has advertised herself as a Republican alternative to Democratic presidential contender Hillary Clinton whose business experience -- and gender -- would give her an edge in the race.
She thinks she can take on Clinton in the realms of foreign policy and national security, given her globetrotting and dealmaking as a chief executive of an international corporation and hands-on experience in advisory roles, such as her work with Hayden.
And she undoubtedly will make the case that her international ventures are an asset in taking on her Republican opponents. Many are governors or freshmen senators who will have a challenge claiming long experience on the issues one handles as commander in chief.
In advisory work with the CIA, Pentagon and the National Security Agency, Fiorina provided guidance on computer data-sharing related to national security issues. And by the time she relinquished her role at Hewlett-Packard, the company was operating in 170 countries, 50 more than when she took the job.
During that time, she visited many of those places and met with leaders of some of America's most prominent allies and rivals.
"Like Hillary Clinton, I, too, have traveled hundreds of thousands of miles around the globe. But unlike her, I have actually accomplished something," Fiorina told a group of Iowans in Des Moines last January, a version of a line she repeats regularly on the stump. In almost every public appearance she references Clinton, and in many instances has specifically challenged the former secretary of state's foreign policy credentials.
Clinton backers critique Fiorina's credentials
Clinton supporters, of course, take a dimmer view of Fiorina's achievements.
Ann Lewis, a senior adviser to Clinton's 2008 presidential campaign, told CNN that Fiorina's private-sector work pales beside Clinton's roles as first lady, New York senator and secretary of state.
"I don't think that compares to the experience you get as a United States senator for six years or certainly of being secretary of state," Lewis said. "It's not really comparable."
At this stage in the race, Fiorina faces long odds of even making it to a debate stage with Clinton, the likely Democratic nominee. Although it's still early, Fiorina's name barely registers on national polls. A CNN/ORC survey conducted in mid-April
showed her garnering just 2% of the vote.
Still, Fiorina has a full campaign team in place. And her travels are a part of her resume that she will mention in stump speeches in early voting states such as Iowa and New Hampshire.
"I sat across the table from Vladimir Putin," she said earlier this month during a gathering of conservative activists in Iowa. "I remember sitting in Bibi Netanyahu's office ... I know King Abdullah of Jordan as well."
"During the GOP primary debates, she's going to be able to name drop like that in a way Scott Walker can't," said Daniel Drezner, a professor of international politics at Tufts University, referring to the Republican Wisconsin governor, who is widely expected to announce his own candidacy. "Fiorina can at least claim to have, in some ways, more foreign policy experience than the rest of the field."
"People underestimate it," Fiorina told CNN, speaking of her foreign policy knowledge. "The truth is, I have a great deal of experience and know a lot of these people who have been in and out of a lot of these countries."
"I'm not shilling for her -- I'm lined up with Jeb Bush as an adviser -- but I would offer you the view that the chief executive officer from Hewlett-Packard has plenty of opportunity to immerse herself in the broader questions of diplomacy, global commerce and global issues," Hayden told CNN. "In fact, one might make the argument that that's as good a preparation as any."
A Bush-trained hawk
In many ways, the Bush administration provided much of Fiorina's foreign policy education. Following the terrorist attacks on September 11, 2001, then-Secretary of State Colin Powell called on her to offer guidance on how the U.S. government could better share data and information between agencies, and she then went on to offer similar service to the Department of Defense and the National Security Agency.
"She was very helpful to the NSA when she was head of Hewlitt," said Robert L. Deitz, a former NSA general counsel and former senior councillor to the director of the CIA. Deitz supports Fiorina's presidential bid.
During the Bush administration, Fiorina sat on the Defense Business Board and the Advisory Group on Transformational Diplomacy for the State Department, which drafted reports for the government agencies from a private-sector perspective.
On the CIA board, Hayden said Fiorina was joined by former members of the Joint Chiefs of Staff, State Department officials, military commanders and a university president.
Foreign policy experts differ on the efficacy and value of such boards, but those experiences undoubtedly provided Fiorina insight into the world of government policymaking, diplomacy and national security that civilians are rarely granted.
"These boards are not significant in that they have an effect on policy, but they are significant in that the members learn a few things while they're on it," Drezner said.
Similar to many advisers in the Bush White House, Fiorina is a vocal proponent of a robust American presence around the globe, a hawkish worldview that lines up closely with Rubio, Graham and Arizona Sen. John McCain.
Like them, she has been blisteringly critical of President Barack Obama's handling of nuclear negotiations with Iran and of Russia's aggression toward Ukraine.
"We need to have the strongest military on the face of the planet and everyone needs to know it," Fiorina told CNN. "America needs to face outward into the world, and I don't think it is helpful to our interests or to the stability of the world when people focus on turning inward."
Last week, Fiorina said that the second phone call she would make as president would be to the Supreme Leader of Iran -- after calling Netanyahu and before phoning Democratic leaders -- to inform him that "there's a new situation in town." Then she would impose "as punishing a set of financial sanctions as we are capable of imposing unilaterally."
When it comes to cybersecurity and information technology, the topics on which she advised the NSA, state and the CIA, Fiorina has little sympathy for fugitive whistleblower Edward Snowden, who leaked classified NSA plans to the media in 2013.
"I think Edward Snowden has been terribly destructive," she told CNN, but added that agencies could be more transparent. "He has been less than forthcoming. It was a very slanted portrayal about what the NSA does, and he knows it."
Fiorina's positions have caught the attention of several conservative hawks. (Fiorina's aides declined to provide a list of her foreign policy advisers.)
"She can go into detail on Russia, China and the Middle East. She has a breadth of knowledge you wouldn't expect from a former CEO," said Bill Kristol, editor of The Weekly Standard.
"Having spoken to a lot of people who run for high office over the years, I think she's way above average and up to a pretty high standard on this."
Her challenge in the primary
Fiorina's international experience will give her an important contrast with her opponents who have served as governors. Though they sometimes participate in trade missions and host foreign leaders, they by and large don't rack up as many international frequent flier miles.
But she will also be running against senators who have served on top foreign affairs committees and can claim more expertise in policy-making.
Still, allies said that Fiorina's GOP opponents should not underestimate her on these issues when they face off over the next several months.
"In any kind of debate," said Deitz, "I'll put my money on Carly."