California's health insurance exchange, Covered California, represents one of the lone bright spots in the troubled rollout of the Affordable Care Act's online health-care marketplaces.
As of last week, California led all states' health-care exchanges at 79,891 enrollments, a 126 percent jump from the previous month, according to data from the state exchanges. The state also led the state exchanges last month, which have operated largely without the same problems as the federal website—HealthCare.gov.
"California is a state showing that it can work," said Peter Lee, the executive director of Covered California, during an interview Tuesday on "Squawk on the Street." "Now we aren't ready to declare success, but we are ready to say, 'it can work if a state gets behind reform.'"
(Read more: Obamacare tech workers will toil on Thanksgiving)
Only 26,794 health-care consumers have enrolled through the online federal marketplace, according to data from the U.S. Department of Health and Human Services. Sixteen states set up their own health-care exchanges, while the rest rely on the glitchy federal website.
Lee told CNBC on Tuesday that his state-run health-care exchange completes up to 10,000 applications a day,
"We're seeing results," he said.
Lee said a third of the California residents applying for coverage will fall under the Medicaid expansion—called Medi-Cal there—and the remaining two-thirds pick the private health-care plans. The federal government pays for all of that expansion for the first two years, and 90 percent after that, Lee said.
(Read more: No security ever built into Obamacare site: Hacker)
While older state residents enrolled in the Covered California exchange at a substantially higher rate than other groups, Lee said he felt optimistic that the number of younger enrolled residents—between 18 and 34—mirrored their share in the general population.
"Young invincibles" are a needed demographic for any health insurance plan, but Lee said healthy 20-somethings alone aren't enough to drive down premium costs. He added that the number of people who successfully enroll this year will determine premiums two years from now.
"The Affordable Care Act gives the nation for the first time the ability to lower health-care costs, which has been basically a millstone around the neck of the entire nation for the last 20 years," Lee said. "Without getting everyone insured, we can't turn our attentions to really lowering costs, which I think we could really do."
—By CNBC's Jeff Morganteen. Follow him on Twitter at @jmorganteen and get the latest stories from "Squawk on the Street." CNBC's Jodi Gralnick contributed to this report.