The website has been online for two weeks. But folks are having trouble signing up.

One person who says she's been trying for two weeks straight to sign up is CNN senior medical correspondent Elizabeth Cohen.

Here's video of her trying and failing to sign up:

"I put in my user name and password and didn't recognize it," she says, showing one example of how she was unable to use the website. "Error messages. Page not found. System down. It's been a tough nearly two weeks for Obamacare."

"I've been trying since day one to get an account and login," she says. "I failed again ... and again ... and again."

Cohen says she's even set an alarm clock for 3 a.m., hoping that she'd be able to sign up then, when traffic to the site would be presumably low. But the system was down at that time.

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