The war is now in its ninth year and is claiming US lives at a record pace as military leaders say the Taliban has the upper hand in many parts of the country.
Eikenberry, the top US envoy to Kabul and a former commander of US troops in Afghanistan, is a prominent voice among those advising Obama, and his sharp dissent is sure to affect the equation.
The options given to Obama will now be altered, although not overhauled.
Military officials say one approach is a compromise battle plan that would add 30,000 or more US forces atop a record 68,000 in the country now. They described it as "half and half," meaning half fighting and half training and holding ground so the Afghans can regroup.
The White House says Obama has not made a final choice, though military and other officials have said he appears near to approving a slightly smaller increase than McChrystal wants at the outset.
Among the options for Obama would be ways to phase in additional troops, perhaps eventually equaling McChrystal's full request, based on security or other conditions in Afghanistan and troop levels by US allies there.
The White House has chafed under criticism from Republicans and some outside critics that Obama is dragging his feet to make a decision.
Obama's top military advisers have said they are comfortable with the pace of the process, and senior military officials have pointed out that the president still has time since no additional forces could begin flowing into Afghanistan until early next year.
Under the scenario featuring about 30,000 more troops, that number most likely would be assembled from three Army brigades and a Marine Corps contingent, plus a new headquarters operation that would be staffed by 7,000 or more troops, a senior military official said. There would be a heavy emphasis on the training of Afghan forces, and the reinforcements Obama sends could include thousands of US military trainers.