"Medicare and Social Security are just blowing up and calculations, which used to be long, dated problems, are starting to come to the fore," Rogoff said. The government's Social Security fund, in particular, will have no choice but to turn to deficit spending, he said.
The state of the environment, he said, will also have consequences for the economy in the coming four years. Rogoff said addressing environmental concerns may require new taxes or caps on pollution.
"To actually deal with it has profound economic implications -- that's why we avoided it," he said. "But we can't wait any longer." The president may also have to tackle the disparity in wealth among the country's economic classes, which, until recently, had reached levels not seen since the early 1900s, Rogoff said.
"Although the recent financial meltdown has gone a long way toward ameliorating those differentials," he said, "nevertheless that remains an issue."
The estate or inheritance tax, which generally applies to the very wealthy, is scheduled to be repealed in 2010. It may prove important to the president's work on income disparity, Rogoff said.
"Repealing the inheritance tax was highly questionable in terms of income distribution and the president needs to address issues like that," he said.
Kent Smetters, a professor at the University of Pennsylvania's Wharton School and former deputy assistant secretary of economic policy at the U.S. Treasury, said that the largest economic issue facing the next president is the "looming entitlement programs."
Smetters said the problems with Social Security, Medicare and Medicaid are much larger in magnitude than the fallout from the subprime housing market and the government's bailout of Wall Street firms.
That bailout, he said, "is just an appetizer for the real deal to come."
He said the problems with these programs today are "much bigger" than what past presidents have faced.
"We've waited so long. You can't possibly increase taxes enough to deal with this problem," Smetters said. "We've actually exhausted all of our black powder at this point in terms of tax increases."
Next up, Smetters said, the president should work to cut the corporate tax rate.
"It's just not sustainable," he said. "We now have one of the highest statutory rates in the world."
India and China have a fast-growing middle class that now has money to invest. "It's going to be a lot less attractive for those countries to invest in the United States and for Americans to keep their money here," he said.
Keeping the tax rate at its current level would hinder investments and growth of our economy, Smetters said.
The third big economic area for the new president -- and Smetters emphasized that it was the third most important -- is the government bailout.
"In my opinion it is a far distant third," he said.
There is going to be a regulatory tangle administering the program and a call for a whole new set of oversight regulations for Wall Street.
But the key, says Smetters, is for the new president to determine what type of precedent the bailout sets for future businesses and investors.
"Does it allow," he said, "for entrepreneurs and corporate executives to game the system?"
Lewis Alexander, chief economist at Citigroup Inc., sees a very significant set of economic challenges for the next president.