Members are told not to discuss the group, reveal the topics discussed in the closed-door meetings, or even say whether or not they are members of the organization.
"You're not supposed to be here," said a grinning Foster Friess, who was pleasant but steadfast in his unwillingness to talk about the group.
An attempted interview with Phyllis Schlafly, founder of the Eagle Forum, was interrupted when a volunteer stepped in front of Schlafly and advised her she didn't have to talk to reporters and guided the conservative matriarch by the arm to her next event.
In the hallways, the talk was of presidential politics, efforts to combat pornography, preserve religious freedoms and fight Islamic extremism.
But for all the mystery, it was pretty mundane, according to those who were inside.
Cheney stuck with a well-rehearsed message on his most familiar topic: staying the course in Iraq.
"For liberty around the world, losing in Iraq is not a good thing," summarized Utah Lt. Gov. Gary Herbert.
Cheney answered questions from the group, fielding questions on immigration enforcement and Iran policy. Cheney said the regime in Iran is hostile to the United States and its allies and that poses a threat in its continual efforts to develop nuclear weapons, according to a source who attended the speech, speaking on condition of anonymity because of the council's strict confidentiality rules.
Romney made family values his central theme, describing how all issues of national security, foreign and domestic policy have their roots in a strong family structure.
"He put an exclamation point behind the importance of the family," said Richard Wirthlin, a former Reagan administration political guru and political pollster. "I think he might have picked up some support in there."
Former Utah legislator and congressional candidate LaVar Christensen said Romney's speech was "sincere, it was substantive and it was from the heart."
Romney was asked tough questions about why he allowed Massachusetts to pass a law allowing same-sex couples to marry and the state's judges to perform the ceremonies. Romney said that he was bound to abide by the state law but took numerous steps as governor to fight for the traditional family.
Cheney and Romney reportedly were given a warm welcome, according to those present.
Phil Burress, president of Citizens for Community Values and a leading anti-pornography activist, said he still questions why, as a board member for the Marriott hotel chain, Romney didn't campaign to have pornographic movies removed from the hotel rooms.
"That's an issue that concerns me about him," said Burress, who has raised the issue personally with Romney. Burress has not endorsed a Republican presidential candidate and said that, despite his concerns with Romney, family values advocates believe he is "head and shoulders" above former New York Mayor Rudy Giuliani.
Utah Democratic Party Chairman Wayne Holland said that the Council for National Policy meeting gives Utahns "a rare opportunity to see - or more accurately not see - what Republicans are all about. And that is how policy is influenced in this country by what amounts to a secret society of far-right-wing conservatives and religious extremists."
Members of the group say they are not a shadowy cabal but concerned Americans engaging in frank policy discussions, made possible by the secrecy.
A confidential copy of the agenda, obtained by The Salt Lake Tribune, showed topics for presentations covering a range of conservative causes, including anti-union presentations, the future of the anti-abortion movement and trends in international terrorism.
Today, the council will hear from Herbert; Rep. Chris Cannon, who will discuss technology and commerce; and his brother, Deseret Morning News Editor Joe Cannon.
Two sessions are also dedicated to Utah's voucher referendum, featuring Doug Holmes, chairman of Parents for Choice in Education, and Lyall Swim, director of operations for the Sutherland Institute.
Featured speakers and topics"Lessons Learned From Utah's School Choice Battle"
Doug Holmes, chairman, Parents for Choice in Education.
"The ABCs of Vouchers: Lessons From Utah's Fight for School Choice"
Lyall Swim, Sutherland Institute
"How Unions Are Affecting the Economy"
Rick Berman, founder of UnionFacts.com.
"Update on the Battles for Worker Rights vs. Big Labor"
Trent England, Evergreen Freedom Foundation
"What is Endangered: Climate or Freedom?"
Va'clav Klaus, Czech Republic president
"How Conservatives Must Continue to Fight the Fairness Doctrine"
Stuart Epperson, Salem Communication Corp.
"The Next Generation of Conservatives"
Rev. Jonathan Falwell
"Resolved: The United States is Winning the War in Iraq"
Debaters: Richard Greco, Jr., Assistant Secretary of the Navy
and John Lenczowski, founder, Institute for World Politics
"Keeping Pro-Life in the Republican Platform"
Colleen Parro, director of the Republican National Coalition for Life
"Parents' Rights in Public Schools"
Mathew Staver, dean of Liberty University School of Law