Yep, I had the same thing happen just a few weeks ago. Unbelievable as to how much they keep trying after I asked questions like: What is your Federal ID#, What is your Tax ID#.  That last one was a good one. They said all the taxes would be taken care of up front, so I didn't need a Tax ID#.  Yeah right I said to them; tell that to the IRS.
Name of the orgainization that called me was WIN Winners International Network.  Calls came from different phone numbers: 876.868.6956,  876.859.5121
They way you win is exactly they way the last person stated. They wanted me to send $600 as well using Western Union or Money Gram.  I told them it was great I won and they could take that money out of my winnings.  They said they couldn't because it was one way it proved who I was to them. They also said that if I didn't hear anything back within 24hours, I should take my receipt and get a refund from Western Union or Money Gram.  Folks; you know very well that is not possible. But these people were as cool as cool and the gang with this storyline.
Suposidly, once they receive your money; They come with a U.S. State Marshal to make sure your not robbed because this is a lot of money.
They will verify and make a copy of your State ID then take you to your bank to have you cash the check so you know that is a legit check.
Becareful here folks.  If they follow through on this; you know very well, someone would come to your door; but they would be fake and taking you to your ATM to withdraw all your money.  Or if you do go to a bank to cash a check; you will soon find that check is invalid; but guess what. They now have your account number.  Don't be fooled.
I even told these people, it is Illegal to request money in order to claim a prize.  Guess, what, not in Jamacia it isn't.  
I called the U.S. State Marshalls office just to let them know they were being used falsely in this scam.  The Marshall told me to fax him a complaint with as much info as I could. I did just that. They flood the Jamacian office with thousands of complaints to the point that they beg for them to stop.  LOL
WIN will also tell you they have offices in the U.S. Ask them to give you one of the addresses.  They will very calmly; but when you look it up on the internet, there will be no such address.  These people are relentless with the lies.
They say if I check out their Federal ID# or with the U.S Marshal or Western Union to see if they are familiar with their firm they say yes they will be.
I said if that is true then I won?t have anything to worry about.  But when I mentioned it again on a Saturday morning call, they got nervous saying they are not suppose to divulge the information out because this is a lot of money and we are not to discuss this business with anyone else that calls.
If I discuss this with them and give her name; which of course was fake, she could lose her job and she doesn?t want her kids to go hungry.
She said she will just donate my money to welfare.  But I had to say on the phone to donate to welfare.  She said they were recording our call.
I also reported them to Western Union and Money Gram and they took a report.
But make no mistake folks.  They could care less.  Why ?  Because they make money off scams.  You have to pay to use their service and like I said before, there is no refund.
When I told them I reported them and the law was on their way; she told me she didn't want to hear it and that I was being a very dificult winner.
I told her, listen, I got enough information from you to report you to the authorities and I had no money to give. She told me they were sending someone to my house anyway. They did have my old address. I told them my "Nine" would be waiting for them-LOL.  
Folks, you can call your phone company and give them up to 5 phone numbers to block. That may help; but know this, most of the time these people are calling from throw away cell phones or calling cards.
oddly enough; the one I called back at the number showing on my phone and the same person did answer. So I think the Law is tracking this down.
Good luck out there and please educate others. It's sad these parasites try and many times suceed in taking money. Mostly from the elderly who don't know any better.  They finally stopped calling me.

i hate Jamaicans. they suck donkey balls and molest children. scumbags and scam artists the lot of 'em.

called and said I'd won 2.5 million. I told them I though it was a scam and they wanted me to give them 650 dollars to pay for the delivery. they said it was going to be delivered by two men and a US Marshal and I was one of 5 monthly winners for using a debit card or credit card or shopping at some business (walgreens ...etc). I told them I didn't have any money to give them and they asked how much I could give them because they could assist me with the charges. I laughed at them and they said they would call me back. Never did.