You did get bait and switched. If it's not in your job description, they can't spring that on you, AFAIK.

Did they say why firing you if you failed to fix something that quickly was their solution? To make you take it seriously, or to actually get it fixed? Once they've fired you, do they have other ways to get it fixed?

Also, do they offer vacation time? Are you allowed to use it?

@thursdaysgeek I can only assume the policy is to make me take it seriously; as far as I know they have no other way to fix it. I get one day of PTO per month.

You don't say how far you live from work, or what kind of traffic problems can happen. Will they pay for emergency helicopter transportation to get you there inside the 20 minute window?

You learned - from what? From your contract, or from a rumor? Please update the question.

Where (in general) are you located? Locale-specific rules will almost certainly be relevant here.

Are you sure it is 20 minutes and then you are fired? I regularly don't notice a missing semicolon within 20 minutes, nevermind debugging a complex situation. As Mono asks, how did you learn this?

"The first time I fail to fix it within 20 minutes, I will be fired." that's an absurd expectation. Imagine you're at the movies, at a bar, participating in a team sport, getting uhhhh... intimate. That's a completely unreal expectation for an endless on-call.

You didn't tag a country, but it may not be legal to require such an intrusive on-call duty without paying you for the time you are on call. See this link. Please note though IANAL.

I've edited the question to answer several of your questions.

"... promoted ... 24/7/365 on-call ... fix it within 20 minutes ..." - If that's even legal, it'd better come with one hell of a pay raise. Did you get a huge pay raise with your promotion, anything that could compensate such a ridiculous responsibility?

Based on the edit, you only assume that you'll be fired if you don't fix something within 20 minutes? No-one has said it to you directly? Seems like you need to talk with your boss and ask them to explicitly list all your new responsibilities, instead of drawing conclusions from one sentence.

What does your job contract say? You must have entered into some sort of agreement with your employer.

As @Moyli points out, it seems you have only overheard some things and are acting on assumptions. Speak to your manager first, and ask to get the rules in writing. Then you'll see...

I can only hope that your salary doubled.

@BЈовић assuming the deal is really "20 minutes or fired" I'd expect at least 5 times the pay. Double pay doesn't cover that you're expected to be available way more than double the 8 work hours. You're supposed to be ready and willing to jump out of bed at 3 in the morning. Ready and willing to stop driving on the highway. Ready and willing to stop your grocery shopping. A large portion of engagements outside work are now unavailable, you are sacrificing even necessities like sleep or food for work. Double doesn't cut it.

8 goes into 24 3 times, so salary times 3...

Have you established if this is seriously what your boss expects from you? I'd speak directly to the Boss about this, don't assume a flippant comment you heard second hand is serious, but don't ignore it either.

@SolarMike you typically work 5 days a week, now they are 7 so it's a 40% increase in number of days worked too so it should be salary times ~4.2. In many jurisdictions working during holidays also requires paying extra compensation.

@GiacomoAlzetta so. according to you, to get 3 8 hour shifts covered you only need a 40% increase in people...

@SolarMike No, I said that if you have N people covering five working days you need 1.4*N people to cover 7 days a week for the same timeslots. going from 8 to 24 hours a day is a 3x increase in time. Going from 5 days to 7 days is an other increase by 40% in time assuming the same timeslots. So going from 8hx5d to 24hx7d is a ~4.2 increase in workload (and in fact in a week there are 168 hours which is 4.2 times 40 hours).

"I found out today when my boss flippantly mentioned it in a conference call with several other managers. Specifically saying "We don't need to worry about the website, we have X on 24/7 on-call now."" - have you confirmed that this wasn't solely a joke/exaggeration?

@GiacomoAlzetta what is absolutely certain is that the OP did not get the commensurate salary increase...

Ok just so we are clear, are you strictly sure you are under this requirement or is this something you've concluded yourself because you overheard your boss? Clear this up!!

Please clarify by editing: have you been actually told you are on call 24/7/365 on-call? From what I understand, that hasn't actually been said to you, or is it? So how are you even supposed to know to be on call always? (Please edit the question to clarify.)

With "moving up the ladder" you're generally more responsible for the overall success, FWIW...