I was perusing Twitter the other day when this turned up in my news feed (written by an American):
Luxembourg must be cross that the UK gets to provide the social services and they collect the taxes from amazon: shelf-awareness.com/theshelf/2013-…
The OED defines cross in this sense as “Ill-tempered, peevish, petulant.” All the citations are British, including Austen’s Pride and Prejudice (1813): “I have never had a cross word from him in my life.”
This is certainly not an unknown word in the U.S. But it is an old-fashioned one, with a rather twee feel to it. Dawn Powell used it (along with a similarly antique verb form) in her 1944 novel My Home Is Far Away: “In the morning he was cross if they waked him.” I associate the word with bordering-on-precious children’s books, as in anthropomorphic bears and ducks who are cross if they don’t get their porridge on time.
As the tweet suggests, the word appears to be getting some broader currency, in part because of the current appeal of NOOBs and in part because it occupies a useful spot on the ever-wider spectrum of annoyance, along with irked, frustrated, and pissed off.
In June 2012, a writer for minnpost.com observed, “Trying to understand all this made me cross.” And health policy expert Uwe E, Reinhardt wrote in the New York Times in March 2013: “I wouldn’t be surprised if the New Jersey hospital industry was cross at me and the commission for our role in the passage of Assembly Bill.”
My favorite recent American use comes from blogger Everett J. Smith, who titled a recent post post, simply, “The Pope Makes Me Cross.”
notoneoffbritishisms.com 
My feeling is that in Britain ‘get cross’ is mainly an informal expression used mostly with family and friends and especially with children. Oxford Advanced Learner’s Dictionary defines it as ‘angry, annoyed’ and Oxford Online simply as ‘annoyed’, which I think would fit your two quotes rather better than ‘petulant’ or ‘peevish’, although ‘ill-tempered’ might do sometimes. In ‘He gets gross very easily’, ‘if you don’t stop that I’m going to get very cross’ – cross simply means angry.
> ‘… gets gross …’??? I get cross with whoever gets gross, hehehe. Yes, seriously though, ‘cross’ means angry, but not to the point of ‘mad.’
Yes, I heard it quite a bit as a child, but this post is the first usage I’ve seen in many a year.
It’s got a bit of a twee association in the UK, too. I associate it with being petulant, so I tend to use it about myself when I’ve got annoyed unreasonably or when I want to insinuate that someone who intends to be disruptive (like a troll, for example) is annoying but not seriously so; saying that someone makes me cross is, I feel, quite patronising to them, as is saying that someone else is cross, which is kind of minimising and dismissive of their feelings. I don’t know whether that’s a UK thing or a me-and-my-friends-and-family thing, though. Some of the examples above sound like there’s something like that going on with them, but the juxtaposition of the serious (eg. Pope) with the small (cross) could just be for humorous effect. I can’t figure that out right now, I’m too tired.
Consider the possibility that “The Pope makes me cross” may also be a pun involving Christian iconography – which would make serious Christians seriously cross.
I agree with the diminutive effect. “Pope gets cross” at least for me conjures up the image of a petulant foot-stamping pontiff. (But “cross with the Pope” just looks like a pun.)
I agree that it tends to be used to children.
Now, do you have “vexed” in the US?
“The Pope makes me cross”—nice use of cross-meaning here 😉
Many people use it as an expression of mild petulance with a touch of humour, as when someone leads you into a succession of slightly irritating events- “Ooh you’re really making me cross now!”
Plenty of American authors – such as Fitzgerald – use it, and as employed by that arch-spouter of “Britishisms”, William Shakespeare, it can hardly be described as “twee”. It’s what Tamora becomes with Bassianus in Titus Andronicus, before having him murdered and his bride raped and mutilated.
I think this comes from the old concept of ‘crossing’ someone, i.e. disagreeing with them or disputing something, or being in direct conflict. It’s the sort of phrase that occurs in historical novels – “Sir Jasper has crossed me once too often!” etc.
Another nice usage is ‘Ooh, I’m as cross as two sticks!’.
In American usage, I associate this with aspirational– if not necessarily upper class– people of the first half of the 20th century. My grandparents, for example, would have used it. And you can certainly imagine a movie heroine in a black and white film saying in that bright, slightly childish, tone they used: “Now look here, Mr. Johnson, I am going to be quite cross with you if…”