IRS Warns of Telephone Scam

I think they should go beyond just letting the user set their own sequence of digits, there should also be an option to have the device generate a random sequence of digits, in a user selectable length, for each call and inject a reading of those digits into the outgoing message at a point in the message selectable by the user (by pressing a button on the device while recording the message).

I have an answering machine that allows for having two outgoing message to choose from.
I have one message that is pretty much what you describe, being something like: "Hello (pause) You have reached the Smith residence (pause) This is John Smith speaking (pause) The wife and I are busy and cannot pick up just now (pause) Leave your name, why you called and a callback number at the tone, and if we think it important enough, we might call you back. (beep)"  I find that I do not get many messages left on my machine with this message (I just cannot understand why) and the few that are left tend to be the tail end of robo-messages that probably started just after "Hello".
If I find myself somewhat curious about who is calling, or want to hear the entire robo-message (to give myself something to report here) I switch to the second outgoing message which is simply: "Hello (pause) (beep)".  I find it somewhat amusing to listen to messages left by real people (or so I assume) that run something like: "Hello, this is Bonnie Clyde for the Fake Fireman's Fund.  How are you today? (pause) Hello? (pause) Is anyone there? (pause) Hello? (click)"  You can often hear the frustration growing in their voice until they hang-up.  Ever so much fun!

Great idea! I'd think four digits would be adequate, with 10,000 combinations. Too many digits, and legit callers might get too frustrated trying to remember them all.

You might think about putting a '1' DTMF tone in your answering machine. This can trigger most robocalls to connect/transfer the call to a person from your voicemail.

The whole point of the robocall is to only transfer the call to the more expensive and limited human agent when a "potential interested customer" presses 1. They are screening you as much, if not more, than you are screening them. Putting that '1' tone in your answering machine helps disrupt that.

It's advertised by a lot of telemarketing companies: https://www.google.com/search?q=press+1+campaign

Yep. I have the "1" DTMF signal on several of my Phone Tray response messages.

"They are screening you as much, if not more, than you are screening them." — That's a good way of putting it.

Scam originates from India or Pakistan, called my house targeting my senior citizen parents. Don’t give them any information and don’t talk to them at all. Don’t return the calls. This is a scam

The message is that I am delinquent in my taxes and that the IRS will have my local sheriff arrest me. We already paid our tax bill and the check cleared the bank. The IRS says they only contact people by US Mail, not over the phone. The problem with all unsolicited phone calls is you have no idea with whom you are talking. This has all the signs of a phone scam.

Definitely a scam.
Even if you did owe the IRS and they were going to issue a warrant for your arrest, they are a Federal agency and it would be a Federal warrant that would be issued and that warrant would be handled by someone from the Federal Marshals Office and not a local Sheriff or your local Police Department.  Fortunately, foreign scammers do not fully understand our system of justice and give themselves away because of that.
If you want to make sure you are talking to a valid representative of a Government agency, or a bank or a credit card company, etc., call them using a valid number from a reliable source (official website, monthly statement, etc.).  If there actually is a problem, they will be able to look it up or transfer you to the department in the organization that can.  Even if you think it may be a valid call, play it safe and tell them "I am busy right now, I will look up your official number and call you back when I can."  More than likely, an invalid caller will hang up before you finish.  A valid caller should accept your statement and not argue with you.  In either case, hang up and call the real offices of the organization the caller claims to be from.

Remember this,  the IRS does not call, if they need to reach you the send a letter via USPS.  Again, the IRS does not call you also if the do plan to arrest you they will not call you first and tell you that you will be arrested.