US president Barack Obama considered halting the daring special forces mission following an intelligence review that concluded there was less than a 50 per cent chance that the al-Qaida leader was in a compound in Abbottabad, Pakistan, identified by the CIA.
On the eve of the operation, only half of his senior security advisers recommended going ahead with the plan, according to the Channel 4 programme.
Mr Obama slept on the problem overnight, and the next day decided it was worth “taking the shot” even though he believed it was only “50-50” that bin Laden was there.
US Navy Seals killed the al-Qaida leader in his secret compound at the start of May in a dramatic raid watched anxiously by the president from the White House Situation Room.
The new documentary, to be broadcast next week, looks at the last-minute debate inside the White House about whether the mission should go ahead.
In late April Mr Obama commissioned a fresh review of the intelligence by analysts from America’s National Counterterrorism Centre (NCTC) who had not been involved up to that point.
The CIA had previously said there was a 60 to 70 per cent certainty that bin Laden was living there, but the NCTC team suggested the true figure could be as low as 40 per cent.
The reviewers were partly sceptical because of the number of visitors to the compound, including some with links to al-Qaida.
John Brennan, the president’s counter-terrorism adviser, said: “It was like, ‘whoa, wait a minute, we thought the prospects were higher of his being there’.
“I think that caused some folks to think, ‘my goodness, we have people now looking at this independently and raising questions about whether or not bin Laden’s at that compound’.
“The president recognised that when people were saying, ‘well, it’s only 40 per cent of a chance,’ that some people were going to get a little bit soft on this.”
There was a crunch meeting on April 28 at which only half of Mr Obama’s aides said he should proceed with the raid.
National security advisor Tom Donilon said: “He received divided counsel. There were some of his most senior advisers who advocated against doing this – thought it was too risky, thought the case too circumstantial.”
Deputy national security advisor Ben Rhodes added: “I think there was a deflation in the room. Because what you’re looking for as you’re getting closer to the call, is greater certainty, not less.
“So essentially it played into all of the fears that people had about what could go wrong – is this worth the risk?”