"I think that the validation there is that people see the potential in action of a company coming into an industry that has had a history of giants, that are slow moving in what they do," Nazemi said.
Insurers who have traditionally dealt with selling insurance to large employers will need to be increasingly consumer-oriented in the era of the Obamacare, according to a Deloitte Consulting report.
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With the introduction of the Affordable Care Act insurance marketplaces, upstarts like Oscar have the ability to compete head-to-head with the established giants.
"You may be able to configure what it takes to make a health plan more efficiently and effectively than a lot of the traditional players," said Deloitte Consulting's Paul Lambdin, who specializes in health-plan exchanges.
Longer-term, Lambdin said, securing attractive provider networks, pricing contracts and managing medical costs will pose big hurdles for new Obamacare insurance upstarts like Oscar.
"They have to bring along providers, and it has to come out at a competitive price, and historically that's worked best with insurers with scale," he said.
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Operating just in New York City, Oscar has managed to contract with a wide network of area doctors and hospitals. It has also contracted with mobile health provider Teledoc, which will allow members to access a doctor any time for free over a phone or computer.
The telemedicine consults may be especially appealing to a younger, more tech-savvy demographic than overall enrollment on New York's health exchange. Since launching in October, Oscar executives say their enrollment has skewed to those who are under age 55.
"Because we utilize technology and data we have ... signals of what's coming in, and we feel that the risk that we have is manageable," Nazemi said.
The upstart won't give any specific enrollment numbers until after open enrollment closes March 31, except to say that it's in the thousands. In their regulatory filings, they had anticipated signing up 7,500 customers this first year, and right now they appear to be on track to exceed that.
—By CNBC's Bertha Coombs. Follow her on Twitter