From the AP article:
One scientist took a cell phone picture of pressure readings and e-mailed it to a government researcher in California for advice.
Just using that cell phone photo, Paul Hsieh, a U.S. Geological Survey scientist, created a model to explain what was happening under the cap and how - despite low pressure readings - there was no leak. He was convinced the containment cap wouldn't blow. He got more data, which bolstered his case.Hsieh, a research hydrologist who normally works with water, labored through the night without the aid of caffeine. He stayed up all night triple checking calculations, going on adrenaline.
"I just knew a decision had to be made the next day," he said. "I had participated in the conference call. I had sensed the tension everyone had and that just kind of kept me going."
Hsieh laid out his case and it persuaded the other scientists to wait.
The government waited six hours, then a day. Nothing happened. The cap held.