Nick Athanassiadis Source: Nick Athanassiadis

He spent a month on an online Obamacare Odyssey. Since Oct. 2, Miami resident Nick Athanassiadis has spent several hours a day—nearly every day—on the Internet repeatedly trying to create an account on the federal Obamacare marketplace to see if insurance plans being sold there might be less expensive than his current coverage. But despite having a long background in digital and software companies, Athanassiadis was repeatedly thwarted by a head-spinning series of glitches, system outages, blank screens, error messages, broken or nonexistent Web links and other hurdles on the HealthCare.gov site that kept his goal out of reach for weeks.

And even when he finally—finally—reached that goal, he didn't like what he saw.

If I were the head of this project, I would have resigned before somebody fired me Nick Athanassiadis

"It's very frustrating," said Athanassiadis, 57, who recorded his online ordeal in more than 100 computer screen grabs and commentary that he shared with CNBC.com. He entitled the odyssey,"Nightmare: A lost month." "I probably have spent two or three hours a day [trying to create an account]. I'm not kidding," said Athanassiadis, who is currently looking for a new job as he pays $750 per month for a Cigna health insurance plan that he began in September. On the first day of visiting HealthCare.gov, for example, he encountered a screen that was meant to have him enter the answers to three different "security questions" that could later be used to verify his identity if need be. But none of the drop-down list of questions had any actual text in them. So "I just gave imaginary answers to made-up questions," he said. (Read more: Obamacare site open for biz, but few visitors)

Another time, his wife became listed, for some unknown reason, as his 10-year-old son's "son/daughter" when he adjusted his entry to apply for an account covering only him and his son, without his wife. Even the toll-free help line that officials urged people with problems on the site to call wasn't able to help him create a usable account for several weeks. "It's horrible. I'm truly ashamed to say the U.S. has come up with this," said Athanassiadis of HealthCare.gov. "If I were the head of this project, I would have resigned before somebody fired me." "If this website belonged to a health insurance company and I had options I would never opt to buy a product or service from this company. I guess, in our case, a lot of us are handcuffed," he said.

In fact, Athanassiadis' experience trying to shop for coverage for his family on HealthCare.gov mirrors those of tens of thousands of Americans who have been unable to create accounts on the website. Unlike a number of states that are running their own Obamacare insurance marketplaces, HealthCare.gov requires that step before showing visitors the true prices of the health plans on sale there. Unlike most of those other frustrated people, Athanassidadis kept running, detailed records of his efforts, which reflect how widespread HealthCare.gov's software problems have been. "The system does not respond in the same manner, time after time," Athanassiadis noted of the multiple problems he has encountered. "Every time, the system seems to be responding in a different way." "The issues with this website are serious, annoying and cannot be dealt with by most users," he said.

(Read more: Obamacare IT chief is out)

HealthCare.gov is the federal government's Obamacare exchange, and is supposed to be selling competitively priced insurance plans to the residents of the 36 states that did not set up their own insurance exchanges as part of the Affordable Care Act. Since it launched Oct. 1, HealthCare.gov has been handicapped by serious software flaws. Officials say that when enrollment data is finally released for the first time next week, it is likely to show that relatively few people have signed up, largely as a result of those tech troubles. But for more than two weeks, the U.S. Health and Human Services Department has been engaged in a round-the-clock effort to fix the site, an effort being overseen by general contractor QSSI. HHS officials have repeatedly said they expect the site to work smoothly for the majority of users by the end of November. But those fixes themselves have sometimes created problems for users, who have flocked to the site because of the Obamacare mandate that nearly all Americans obtain health insurance by March 31, 2014, or face a tax penalty. (Read more: Insurance canceled? Don't freak out) "While the company is trying to fix issues, they break other areas that used to work," Athanassiadis said. "The system goes down frequently or responds in a different way than previously, creating another layer of confusion and annoyance for the users." In a conference call this past Monday with reporters, an executive with a contractor involved in the repair effort on HealthCare.gov acknowledged that the most recent outage to the site's application and enrollment function was a result of upgrade efforts. "These outages are not unusual as things on HealthCare.gov are improved," said the executive, Andrew Slavitt, executive vice president of Optum, which owns QSSI.

HealthCare.gov website experiencing outage. Source: HealthCare.gov