From the WaPo story:
The U.S. ambassador in Kabul sent two classified cables to Washington in the last week expressing deep concerns about sending more U.S. troops to Afghanistan until Afghan President Hamid Karzai's government demonstrates that it is willing to tackle the corruption and mismanagement that has fueled the Taliban's rise, said senior U.S. officials.
From the NYT:
Mr. Obama asked General Eikenberry about his concerns during the meeting on Wednesday, officials said, and raised questions about each of the four military options and how they might be tinkered with or changed ... [Senior] officials, who requested anonymity in order to discuss delicate White House deliberations, did not describe General Eikenberry’s reasons for opposing additional American forces, although he has recently expressed strong concerns about President Hamid Karzai’s reliability as a partner and corruption in his government.
I presume that Ambassador Eikenberry's concerns today are more or less the same as the ones he expressed during testimony before Congress in 2007:
Army Lt. Gen. Karl W. Eikenberry, the outgoing top U.S. commander in Afghanistan, also warned that an even greater threat than the resurgent Taliban is the possibility that the government of President Hamid Karzai will suffer an irreversible loss of legitimacy among the Afghan population.
-- snip --
"The long-term threat to campaign success . . . is the potential irretrievable loss of legitimacy of the government of Afghanistan," he said.
"The accumulated effects of violent terrorist insurgent attacks, corruption, insufficient social resources and growing income disparities, all overlaid by a major international presence, are taking their toll on Afghan government legitimacy," he said. "A point could be reached at which the government of Afghanistan becomes irrelevant to its people, and the goal of establishing a democratic, moderate, self-sustaining state could be lost forever."