Obamacare needs 'sexy' makeover: CEO

Healthcare.gov plagued by problems: CEO

The only way to get more Obamacare signups is to significantly reduce the scope of the legally required minimum plan, athenahealth Chairman and CEO Jonathan Bush told CNBC on Friday.

The White House took a temporary step in that direction late Thursday, when it relaxed the rules for people who lost their existing coverage, because their plans didn't meet the health law's broader standards.

(Read more: Feds offer another break to people losing health coverage)

The changes allow those affected to buy cheap, basic catastrophic coverage plans, and waive the threat of a tax penalty if they fail to have any coverage in 2014.

Bush, whose company provides doctors offices with cloud-based services for electronic health records, practice management and care coordination, said on "Squawk Box" the Obama administration needs to narrow the requirements of the mandated plan by half to make it more enticing.

"You'll have a very different cost curve because the only way you get people into the market is if you make it sexy and attractive and affordable," he said. People are willing to "dump about $200 or $300 a month into this thing" for something closer to catastrophic coverage.

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As for the troubled federal Obamacare website, the administration hired former Microsoft executive Kurt DelBene to oversee the ongoing fixes. He's replacing management guru Jeffrey Zients, who was tapped by the president in October to manage the emergency repairs.

(Read more: White House names former Microsoft exec to run Healthcare.gov)

"The federal government will pull off the operation of a website. It will always be lame. It will never be a marketplace," Bush said, adding sarcastically that the White House was able to "get the guy who ran desktop Microsoft Office to create the Amazon of federal purchasing."

"I think about a third of the people will pay the fine" for not purchasing coverage, he continued—including healthy young adults, people who don't make a lot of money and those who "don't want to sit for two hours on a website and feel like they're at the registry of motor vehicles."

By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.