Many Argentines have expressed concern at her being sidelined only three weeks before congressional elections, just when US Supreme Court rejection of an Argentine appeal makes another debt default more likely, the economy has slowed sharply, and her Vice President Amado Boudou is under investigation for corruption.
"This is no time to go on automatic pilot," economist Jorge Todesca said in a letter to his clients.
Todesca said Fernandez has run the government like an "anarchy" characterised by spontaneous acts, short-term thinking and key decisions that she often makes from within an intimate circle of advisers.
Without her daily presence, top officials could lack the political authority they need to manage a looming economic crisis, he said.
Fernandez's doctors said she suffered no complications from their removal of a blood clot from the surface of the right side of her brain on Tuesday. But their brief post-surgical report made no reference to how long the president would need to rest or how much Argentines could expect from her in the meantime.
Some outside experts said that patients can need as much as three months to recover from such surgeries, and that only time will tell if her still-unexplained head injury caused lasting brain damage. Others said the 60-year-old leader could be safely back at work within days.
Brain surgeon Rolando Cardenas, who directs the Stroke Committee of the Argentine Cardiology Society, said she'll likely need to keep a drain in her skull and remain in intensive therapy for up to three days.
If her headaches, muscle weakness and numbness disappear by then, "her recovery time would be shorter. In that case I estimate that in about 45 days she could return to full activity," Cardenas said.
Former US President Ronald Reagan suffered a similar injury when he fell off a horse after leaving office, and quickly recovered from surgery to remove the blood clot at the Mayo Clinic, said Dr John H. Sampson, a brain surgeon at Duke University.
"The Argentines don't have to worry that they're going to be without a president for any period of time. Literally, within a week she'll be back in the office, very competent and with no risk," Sampson predicted.
But Kevin McGrail, the neurosurgery chairperson at Georgetown University Hospital in Washington, said the irregular heart beat that Fernandez suffers could complicate her recovery.
Fernandez's office has not released any details about any drugs she may be taking, but arrhythmia patients commonly take aspirin or other blood thinners, and these anti-coagulants would have to be stopped for her brain to heal. That increases the risk of a stroke, so she'll need to be careful, McGrail said.
"If she's on a blood thinner, that would cause a whole other set of problems, and it would explain a lot of things, because she's a little young otherwise for a chronic subdural" hematoma, McGrail said.
Dr Claudio Santamaría, who runs Argentina's Superior Institute of Health Sciences, agreed that Fernandez shouldn't take any aspirin or anti-inflammatory medicine that could cause more bleeding. And while only 10% of patients suffer complications following surgery, he urged that she not try to do too much too soon.
"She can't travel by car for two to four weeks, because the movements and the braking can re-injure the wound," he said, adding that she should avoid exercise altogether for three months.
Neurologist Gabriel Persi, meanwhile, said the president should rest as much as possible to avoid stressing her heart.
Fernandez's spokesperson, Alfredo Scoccimarro, said the next medical report would come at midday on Wednesday, and left the hospital steps without answering questions about her condition.
While Boudou clearly assumed control of the executive branch, the presidency didn't release a formal transfer-of-power document indicating how long this situation might last. Boudou said he and other top officials would run Argentina as a team "while she gets the rest she deserves".