Story highlights Callers to the 800 Obamacare number must wait weeks for a mailed statement

One they receive it, they are told to call back

Callers can't get any information about options without the statement

Health insurance enrollment is just a phone call away.

At least that's the message President Barack Obama and Department of Health and Human Services officials have been pushing as an alternative to the embarrassing technical challenges with the enrollment website.

To see just how easy -- or hard -- enrolling over the phone would be, I called the 800 number Obama provided in his Monday speech.

"Average wait times for calls is less than 30 seconds, and 3 minutes for chats," wrote Secretary Kathleen Sebelius on the HHS blog Thursday.

It all sounds so easy, right? Not quite.

Sebelius was right about the wait time. I was able to get a person on the phone in less than a minute.

They told me we needed to first get set up with an application. That part was very simple too — I was asked basic questions like my name, address and Social Security number.

Five minutes later, they said I was I all set.

So did that mean I was enrolled? No.

I have to call back-- in one to three weeks -- for that.

Turns out, the call center can't actually process applications over the phone. They can just take your information and submit it for you.

Once I get a paper statement in the mail saying I'm eligible to enroll, I can then call the center back and enroll over the phone, the representative said.

From a consumer standpoint, the most frustrating aspect was that I couldn't get any specifics about the various insurance options during this call either.

I was told they can't divulge the information about the four levels of coverage choices until I get that piece of paper in the mail -- a long, drawn-out process for something that it appears could be done immediately with technology.

"No one gets new benefits until January 1st," said Sebelius on Friday at an event in Austin, Texas. "And if an individual signs up by the 15th of December, they will have coverage on day one."

Based on my experience, there should be an asterisk by the December 15 date. At least in terms of calling to enroll over the phone, which I quickly learned is a several-step -- and several-weeks-long -- process.