After getting only four calls from these people, I called them back asking who they were. Naturally, they began on their spiel about me being pre-approved for this and that. I lied by telling them I was only 16 and had just a Savings account. They told me I wasn't qualified and removed my number instantly -- they said it might take up to 48 hours to stop receiving calls, but after that call, I didn't receive another one, and it's been almost a week now.
If you think about it, they aren't going to want to mess with calling someone so young, not only because there's no business to be had (no Checking account, which apparently their entire platform thrives on), but also since doing so might put them into even more of a legally questionable position... even if they may think you're not telling the truth about being too young, they're probably going to choose not to take the risk of continuing their incessant calls.
Tell them to stop calling your teenage daughter, tell them you are a teenager, whatever you feel most comfortable doing (I'm 19 so this was easy to pass off -- it was only over the phone anyway). Sound friendly or at least indifferent, and be sure to emphasize that you don't have a Checking account either. If you get a persistent operator, simply hang up and call back, and you're almost certain to get someone new on the line. Above all, don't divulge ANY personal information other than the number you want removed (which they clearly had in the first place).
As a preventative measure in the future (and likewise to those who haven't been struck by this yet), add your number(s) to the National Do-Not-Call Registry at
http://www.donotcall.gov/ - this is GUARANTEED protection against these calls, but takes about a month to go into effect, so don't hesitate. These people WILL follow this list, because the consequences for not doing so are SEVERE. It's my gathering that violators can be fined up to $1,500 PER INFRACTION (and I believe an infraction would constitute a single call; correct me if I'm wrong). It'd also be very easy to prove violations -- all that would have to be done is a subpoena to a victim's phone company to find out when a call was placed, and then crosscheck that entry against the Do-Not-Call Registry's database of people who have opted out.
One last thing - the number they called me at is relatively new and has been given to very few, and only trustworthy sources. How they mined this number, I have no idea... sequential dialing sounds ridiculous, but it's the only thing seems even remotely plausible to me. I'm still curious about this phenomenon though, so if anyone has any idea where these people are getting phone lists, do tell.
Good luck to all!
-Ben (Lincoln, NE)
P.S. - For the sake of public knowledge, here are the four calls I received (yes, they called twice on Independence Day, and that's the same day I was removed):
July 3, 2006 @ 10:52 am - 888-669-8868 - Not answered
July 3, 2006 @ 4:55 pm - 888-669-8868 - Not answered
July 4, 2006 @ 10:18 am - 727-544-0057 - Not answered
July 4, 2006 @ 10:40 am - 727-450-0346 - Not answered
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I was called about this scam, however the number was different. The number was 727-596-8705. I got the same line as everyone else. My name and number was pulled out of a box at a large mall in my area. this couldnt possibly be a scam, or so that is what Aaron, the rep said to me. Today my account was debited for 129.00 and I was livid... I did agree to the program, however after reviewing and researching this place, I soon realized that I had made a huge mistake. I called the phone number that I had for them and the lady literally told me that the company was being moved and she was being asked to get off of the phone so that they could take the phones off of the walls. I was alarmed and told her that I wanted to speak with a customer service agent. SHe then told me that there was only one lady and she was moveing. I began questioning her using questions like why is there only one CSR for such a large and established business? She of course couldnt answer and said that she had to go because her phone was being pulled out of the wall.. I would curse out anyone who called me from this place and you should too.. They are crazy...
I just contacted the Customer Care # provided and got more details on what the $129.95 was paying for. Of course, I got this scripted response and going around the question. So I started asking more detailed questions like: How can they guarantee me at least $500 credit limit without a deposit? Are they going to just submit my info to a bunch of creditors to see who will reply? etc... They replied by telling stating that they don't submit any info. All they do is send you a list of credit card companies and I have to submit my own info. I then asked how can they guarantee my credit limit if they are not submitting my info? They only guarantee that i will be approved by one of the twenty creditors that i have to apply for. I then asked what if not approved by any what happens? They stated that if denied by three or more companies they will refund moneys after i send the denial letters to them by mail and the processing for refund is upto 6 wks once they received all info needed. I then asked to do i go about canceling my transaction? They placed me on hold for at least 15 min for a manager (which i think was to see if I will hang up, which I didn't) Manager got on the line to confirm i wanted to cancel and then placed me on hold for another 15 mins (doing the same thing) They finally got back on line and completed my cancellation transaction. So now all i can do is wait and hope no money is taken from my account. 
. Like I told them, I can go online and do what they are doing for free. And to PLEASE DONT CALL ANYMORE. We'll see!!!