We received a series of harassing phone calls attempting to convince us that we had won a cash prize, even going so far at one point to claim they represented the Walmart Sweepstakes Prize department.  The pair (one claiming to be a manager) indicated that they were from "Las Vegas, Nevada City" and that I could follow up by calling 206-259-6727 (a Seattle area phone number, probably chosen at random as he seemed to make it up as he was giving it to me).
I warned them not to call any more and that I would involve the FTC and the FBI if they continued.  They persist.  I'm now posting warnings and filing complaints with the aforementioned agencies.  Phishing is particularly illegal since the 2004 legislation passed to make it a crime.  Unfortunately, as these calls are coming out of Jamaica (1-876 prefix being Jamaica), there is likely little repercussions to these folks.  They have probably hacked the local phone system and are calling internationally with no charges to them.  Any money they obtain from phishing is probably gravy as they likely have nothing better to do and no prospects for making money honestly.
As a warning, they persist without reason (other than chasing your and my money).  Trying to reason with them or threaten legal action is pointless.
The best recourse is to simply hang-up and not take their calls.

caller id reads: CELL PHONE JM
caller left a message that there is something 'important' to discuss.............
these Jamaicans robo-callers are at it again......
I recommend giving them the silent treatment.
Do not answer the phone as that tells them your phone number is valid and they will pass your number along to the next robo-calling company.