With the Obama administration considering a reshuffling of top energy jobs in its second term, former administration officials and political heavyweights from both parties are calling on the White House to craft a national energy strategy, an elusive goal since Richard Nixon was president.

The push reflects the unprecedented and unexpected boom in domestic energy production in recent years, with the U.S. poised by some estimates to surpass Saudi Arabia as the world's top oil producer by 2020.

The energy renaissance, due to the new technologies of hydraulic fracturing and horizontal drilling, has made electricity and natural gas cheaper for consumers and manufacturers. But the opportunities for the economy and national security presented by the flood of oil and gas stand in contrast to the fragmented policy-making and oversight of the industry.

Decision-making involving energy resides in various parts of the bureaucracy. The State Department last year was charged with deciding whether to allow the Keystone XL pipeline to transport oil to the U.S. from Canada, while the Department of Energy's Office of Fossil Energy is currently deciding whether to allow large-scale natural-gas exports.

"In a government that has 20-some agencies that have a piece of energy policy, how do you make some sense of that? This is like an orchestra without a conductor," said former Sen. Byron Dorgan, a North Dakota Democrat.

Mr. Dorgan and former Sen. Trent Lott, a Mississippi Republican, have been making the rounds in Washington pitching an idea from the Bipartisan Policy Center, a think tank, for a national energy strategy council modeled on the National Security Council.

"Now is the opportunity, at a fantastic time of challenge for us, to develop an overall national energy policy…and not wait for another crisis," Mr. Lott said.

Both the Department of Energy and the Environmental Protection Agency were created in the 1970s during a different economic and geopolitical climate, when the U.S. first confronted its dependence on Middle Eastern oil imports.

"Energy security is national security," said Sen. Jeanne Shaheen (D., N.H.) during a Senate debate last week on Pentagon energy policies. "Energy security is going to require an all-of-government approach."

Gen. Jim Jones, the Obama administration's first national-security adviser, helped shape the Bipartisan Policy Center proposal. He said the goal is to bring to energy policy the same "rigor, seriousness, and consistency" that characterizes U.S. national security policy.

Sen. Roy Blunt (R., Mo.) said the U.S. leadership role in the world depends on economic strength, which in turn depends increasingly on energy resources. Other countries, he said Monday, "understand that they benefit from a strong, dependable, secure U.S. economy, and energy is a key to that."

The personnel turnover likely in the early part of the Obama administration's second term offers a chance to recast policy.

Energy-industry officials and environmental groups say they see Energy Secretary Steven Chu and Environmental Protection Agency head Lisa Jackson as likely candidates to step down, although the administration is skittish about fresh confirmation battles in a polarized Senate. Neither Mr. Chu's or Ms. Jackson's office returned calls seeking comment.

Outside energy watchers say Mr. Dorgan, the former senator, is one possibility for the Department of Energy job. Other names mentioned include Dan Reicher, a former Clinton administration energy official who headed energy initiatives for Google Inc., GOOG -1.05% and former Clinton chief of staff John Podesta. Representatives for the three didn't return calls seeking comment.

A group of business leaders and former military commanders on Monday called on the government to embrace both greater domestic production and promote technologies such as natural-gas vehicles and electric cars to cushion the economy from shocks associated with oil prices.

"The U.S. has the potential to reduce our dependence on imported petroleum, and thereby reduce our national security risk, to improve our balance of payments, and to increase our GDP," said Fred Smith, chief executive of FedEx Corp. FDX +0.71% and co-chairman of the group.