American Publishers Service Bate and Switch Morristown , Tennessee

A few months ago I received a call from American Publishers telling me that I had won a $1000 online shopping spree and that in order to receive it they would need a debit card number.
I ignorantly gave it to them not really thinking that it was a scam. They then offered me 3 magazines a month for approximately 5 years. I would only have to pay $19.90/month for the first 30 months and that would take care of the last 60 months so that I would not have to worry about making payments after that.
 They then asked me to verify my credit card number. I do not remember having agreed to or picking out any magazine subscriptions. However within couple of weeks they tried to take money out of my husbands account, the bank called him to ask permission for the payment and another one that had been request by United Benefits. My husband put a stop on the payment.
 Within days they started calling my phone constantly and, although I do not remember having signed up for this or picking out the magazines, I started receiving magazines. Then I started receiving their bill in the mail.
While trying to discuss with my husband what we should/could do they continued to hound my phone and tell me that if I did not make good on my account they would be sending it collections.
Finally my husband and I decided there was nothing we could do since they told me I could not cancel the subscriptions. Yesterday they called again and I finally just gave in and gave them MY card number since I was told there was nothing I could do about it.
I cannot afford almost $600 on my credit! I have no idea what to do now! I do not need or want these magazines! Also I never receive the so called $1000 online shopping spree they originally called me about.
I just don't understand how companies can do this to people! So now I am out $19.90 a month for pretty much the next 3 years! Nearly $250 a year. That may not seem like that much to some people however, our income was the entire reason I was excited about the so called $1000 shopping spree!
 Do you know how many diapers, clothes etc I could have bought for my children with that! And they called me right before Christmas as well! I feel like I have been played! I don't even know if there is anything I can do now that I gave them my new card number.
I've debated putting a stop on the payment and just letting them send it to a creditor. I just cannot handle the stress of their constant phone calls and it seems like they are always calling from a different toll free number.
I wish I would have done a search on them earlier.