Through no fault of his own, Obama will not be joining them.
The first requirement of presidential greatness is that the country faces a mortal peril, something that puts the America experiment - its embrace of freedom and equality, its trust in democratic institutions, and its belief in itself - at risk.
The great presidents have all defused that risk.
In 1789, no one knew whether the Constitution would survive; Washington's stature inspired loyalty that gave the system permanence.
Lincoln's single-minded pursuit of total victory over the Confederacy - when many in the North, discouraged by the endless bloodshed and inconclusive combat, wanted a truce - saved the Union and ended slavery.
FDR preserved the nation's democratic political values and institutions in the face of an economic collapse that gave rise, from left and right, to calls for radical change; and, of course, he presided over victory in World War II.
Obama will be denied a similar opportunity because, for all the nation's serious problems, none yet rises to the level of mortal peril. Obama's reputation will necessarily be less exalted.
He is probably fooling himself if he thinks Obamacare, by itself, ensures him a spot close to the top in the presidential rankings.
Medicare and Medicaid (far larger insurance expansions) didn't do that for LBJ, so why should a lesser achievement do it for Obama?
Indeed, if the implementation goes badly (coverage overestimated, costs underestimated), Obamacare could backfire.
Still, Obama's enthusiasm for it is telling. Even without the 2008-09 financial crisis, he would have arrived in office just when the retirement of baby boomers was slowing the economy and raising - through Social Security and Medicare - government spending.
The cost of government was increasing; the capacity to pay was decreasing.
In these circumstances, Obama chose to expand government. His frame of reference was backward-looking: the fulfillment of a liberal agenda conceived from the 1930s to the 1960s.
But history's verdict will be present-oriented and forward-looking. How have his fateful decisions played in the real world?
Obama's reputation will ultimately depend on a handful of these, including (probably) his handling of the economy in the dark months of early 2009, Iran's nuclear program, the federal budget and, perhaps, something now unimagined.
"Crises demand leadership," writes Merry, "and in the American system that leadership can come only from the president."
Not just leadership, but leadership in the right direction.