The scam works like this: a person calls you up claiming to be from the state or county or court or whatever government entity, and says that you missed jury duty, which is a serious offense. Then, they tell you to pay some amount now over the phone, or else you'll face some sort of penalty, like public humiliation or being arrested or larger fines. The amounts vary with reports indicating some scammers demanding as little as a hundred dollars, while others demand over a thousand. Also, notably, this scam has gone digital and is also perpetrated via email.
Generally, if you miss jury duty, or are in legal trouble, you are not going to get a phone call. Maybe if you were actually selected to serve on a jury and you don't show up, or you mouth off to a judge on your first day of service, you might get a call from an upset judge or frustrated bailiff, and get in some real trouble.
However, it is highly unlikely that you'll get a call if you fail to show up for jury duty, and even more unlikely that the caller would demand money. Also, if you do get a call from law enforcement, or a government official, generally, they will want you to come in to the official location, like the court, police station, or city hall, rather than just pay money over the phone.
The Government Paper Trail
When paying any governmental fine, it will almost never happen that you won't receive some sort of receipt for the payment. Additionally, if you are paying a fine or penalty to the government, you absolutely need to have documentation to show the fine is legitimate and that you paid the fine.
So again, do not pay the government for alleged fines over the phone unless you are the one calling them and you are 100% positive you are calling an official government office.
But What If ...
No. No. No. And No. There are no "what ifs" here. Do not pay the government over the phone if they call you. Not for nothing. While some government agencies do accept payment by phone, they'll send you an official paper bill that explains how to pay by phone first, and won't hound you for a payment or threaten you if you can't make the payment.
Scammers have been using all sorts of different government impersonation scams since the very inception of scams. Now, the dumbest of smartphones can be used to impersonate government phone numbers on caller IDs.
If anyone that you don't know calls you and demands money, you should probably search the internet to make sure you are not being scammed before paying them anything. A big red flag should go up if they ask for payment via gift cards, iTunes gift cards, or prepaid visa gift cards (if you are asked to pay via one of these methods, you are likely being scammed).