I've bundled up my comments into an answer of sorts. (ha, it looks worse than the comments - who chose these colours and fonts?)
In British English (or rather in Britain) I've certainly heard aren't we etc used in that way. Whether it is right/proper/by the rules/grammatical/whatever I have no idea .
One of us is wrong, aren't we?
It's got a question mark, but it's not used as a question, it's used as a statement and that particular statement means You are wrong but I'll leave it to you to tell me that it is you who is wrong.
That format is commonly used in a condescending manner or when talking to children.
One of us was breaking the speed limit, weren't we Sir?
meaning You were breaking the speed limit.
One of us is heading for a smack, aren't we?
meaning You will soon get your bottom smacked if you don't stop what you are doing
And in the case of the original question
One of us is going to have to start talking, aren't we?
meaning I'm going to start talking but I've said this in an introductory fashion so as not to appear too forward
But then, there's the balls...
One of these balls is blue, isn't it?
Is pretty standard I'd say, it might be rhetorical or it might be a proper question that needs an answer to someone learning colours.
It could even be a test for someone who has difficulties with words and/or the balls are actually red and green.
This version however
One of these balls is blue, aren't they?
I don't think I've ever heard a question posed like that (in BrE).
Lengthy further discussion on comments summarized here just in case a raft of comments get deleted, but we all know that never happens, don't we?
Can we use One of us is wrong, isn't he? without any sarcastic or
patronizing undertone? Just as in Well, we can't both be right, so
surely one of us is wrong, isn't he?
Is there sarcasm in well, at least one of us dodged that bullet,
didn't he? Am I correct is started to wonder about a specific
idiomatic use of aren't we that has nothing to do any more with the
actual normal formation of question tags
If you said One of us is wrong, isn't he? who would be the he in that sentence? If there are only two of you, then calling the other person he instead of you is wrong, it should be one of us is wrong, aren't you? which is quite blunt. If there were three of you, you could ask the third party One of us is wrong, is it him? not quite so blunt but not quite as clear as the simple Is he wrong?
The aren't we on it's own isn't enough to add the sarcasm. In combination with the statement the aren't we means and I (the speaker) know who that is going to be. So it's sarcastic when used with one of us is wrong but not sarcastic when used with one of us is going to have to speak first.
One of us is wrong used with aren't we has almost always got a sarcastic undertone. Without sarcasm it would just be We're wrong or One of us is wrong or One of us is wrong but I don't know which. In that particular phrase I would always assume the aren't we is sarcastic. It's a very fine line though and the intonation of the speaker is very important.
Can this irregularity also appear with or the singular subjects that
get a plural question tag? And does this ever happen anywhere else
than in question tags? Is "One of us is wrong. He should apologize."
also wrong?
That's slightly different. You could just about say that to a third party (imagine two children A & B are arguing and talking to their mum). Those two sentences (spoken by A) are suggestive that A thinks B is wrong and adds He should apologise to add emphasis to their belief that B is wrong. If it were only two people then it would be completely wrong to say that, you would never address the other person as He.
However, in the UK if you were stopped while driving by the police they would always ask Have we been drinking tonight Sir? They use the we to mean you in the same way the we is used as you in One of us is wrong, aren't we? which really means One of us is wrong, aren't you?
Tip : Never answer the policeman's question with I don't know, have you been in The Bull and Bush sinking pints for the last eight hours too?, sarcasm only works one way with the police.
An example with no sarcasm whatsoever
One of us is going to have to work tonight, aren't we? That's not sarcastic if one of you does have to work tonight and neither of you know which one it'll be.
And the application of sarcasm
If you DO know it's your friend that has to work you can say One of us is going to have to work tonight, aren't we? that's sarcastic.
And in a not sarcastic manner to avoid a blunt statement
Similarly a boss could easily say to a worker One of us is going to have to work tonight, aren't we? and both parties know it means You (the worker) are going to have to work tonight. That's what I mean about it being a statement and not a real question.
It's definitely a 'trick' used to avoid saying a blunt statement or to give someone the opportunity to admit to something without it appearing forced so perhaps it is only used with 'questions' but as seen above it can be used in a direct meaning where two people are unsure of the outcome.
I'm not sure how different it is in AmE but I'll say that the Americans I know have no problem with this form but they are used to hearing it so they aren't a good test for BrE/AmE differences.
Best Answer
If you want to know what native speakers would do, ngrams is always a good start.
Conclusions:
So "what are needed" is very rarely used, and when it is used it is exclusively used with are rather than is.
This also matches with my personal experience and what feels right to me.