There was the following paragraph in the article titled “How Russia wants to undermine the U.S. election” in Time magazine (October 10):
One day in June she (Arizona Secretary of state, Michele Reagan) was
in her backyard in Phoenix when she got a call from her chief of
staff. “Are you sitting down?” he asked. —A group of hackers
known as Fancy Bear was trying to sell a user name and password that
belonged to someone in Arizona county election official’s office,
which holds the personal data of almost 4 million people “My reaction
was, well, this is like the worst thing that you want to hear,” Reagan
recalls.
In other source – motherjones.com. (October 8), the phrase, “Are you sitting down?” is rephrased as “Can you sit down?'”:
Arizona Secretary of State Michele Reagan was in the backyard of her home last June when she got a call from her chief of staff. "The first words out of his mouth were, 'Can you sit down?'" Reagan told Mother Jones. He then said that her office had been "contacted by the FBI, and it looks like there's a computer password and username that belongs to our database for sale on the dark web."
http://www.motherjones.com/politics/2016/10/state-election-hacks-undermine-voters-confidence
Are “Are you sitting down?” and “Can you sit down?” used to try somebody to brace for a shocking news, or calm down the other in advance?
What do they exactly mean? Are they very popular turn of phrases?
Best Answer
Yes, that's what it means: "be prepared for some bad or, paradoxically, very good news I'm about to break." It's an introduction to the news someone is about to break over the phone and a reference to the possibility they may faint or have any sort of untoward symptom when they experience intense surprise, fear or shock. If one is sitting down, they are less likely to get hurt.
Examples of cases where you'd ask "are you sitting down?" before breaking the news:
As we can see from the examples, it has more to do with "intense surprise" than with the news being good or bad.