It's a crucial time for Obamacare. Here's why

New health care delay

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?)

Another question remains over how many of the potential health care consumers who return to the relaunched website fall into the coveted "young invincible" demographic. Democrat Howard Dean, the former governor of Vermont and CNBC contributor, predicted that 20-somethings might eventually sign up out of a fear of crippling health care costs from an unforeseen catastrophe.

"It's the 26- to 30-year-olds you have to worry about here," Dean said Friday on in a "Squawk on the Street" interview. "And I agree there will be some resistance to signing up here, and they eventually will. And not because of the ... fine, but because it makes sense. If you may have spent the money on a Harley Davidson, that will get taken by the debt collection agency if you get sick."

The outcome of this weekend's relaunch will largely become a public relations issue, Dean said, highlighting that millions more people will receive Medicaid coverage in states that expanded the program to lower income pools, and "everybody knows how to make [Medicaid] work."

(Read more: Obamacare rationing coming? No doubt, analyst says)

The Healthcare.gov website is displayed on laptop computers.
Andrew Harrer | Bloomberg | Getty Images

"At this point it's all optics," Dean said. "Either the website works or it doesn't. If it doesn't, the Democrats and the president are in a lot of trouble. And if it does, it's going to be a big boost because 30 more million people are going to have health insurance."

The question over younger demographics also weighs heavily on Alan Miller, the CEO of Universal Health Service, which runs about 200 hospitals nationwide. Miller said insurers worry over whether younger people begin signing up, but added that the expanded coverage will benefit his company.

Miller said the initial roll-out problems could continue for months, however.

"I don't know how long that lastssix months perhaps," Miller told CNBC. "But ultimately it will get fixed. The coverage will be expanded and that will be very good for the industry and very good for the people in the country."

(Read more: Obamacare: CNBC Explains)

—By CNBC's Jeff Morganteen. Follow him on Twitter at @jmorganteen and get the latest stories from "Squawk on the Street. Reuters contributed to this report.