Of all the questions hanging over the troubled rollout of President Barack Obama's signature health care law, one looms larger than the rest for former Health and Human Services Secretary Mike Leavitt.
"How quickly people will come back is a mystery to all of us," Leavitt told CNBC on Friday during an interview on "Squawk on the Street."
The Affordable Care Act and its glitch-prone online marketplace face a serious stress test this weekend when the Obama administration attempts to meet a self-imposed deadline to fix the healthcare.gov web portal. Only about 27,000 users successfully used the website in its first month, out of the millions who tried to access it.
Leavitt, a cabinet member of George W. Bush and former governor of Utah, told CNBC that the relaunch risks giving more fuel to the president's critics if it doesn't go off seamlessly.
"One of the dilemmas that the administration found themselves in is that they had to put out a [certain] date," Leavitt said. "But they created such expectation now around this date that in some ways [it] would be hard to meet. If everybody doesn't see it as perfect, they will have failed."
(Read more: The second coming of Obamacare website—will it work?)