Should there be a comma before the word "until" in the sentence below?

Solution 1:

I would say that there should definitely not be a comma there. A comma would give the implication that the words after the comma are 'not essential' or are 'additional information'.

But, in fact, the words "until Friday" are absolutely essential to the meaning of the sentence. There's a big difference between these two sentences:

They are not taking their team photograph.
They are not taking their team photograph until Friday.

I agree with the comment that there could be an optional comma after "Friday".

Solution 2:

In

We are staying here until Friday.

there is no need for a 'breather' comma to help the reader. Is there a syntactic need or a sensible reason for inserting a comma there?

There possibly is – it depends on whether you want to emphasise the temporal adverbial or not.

We are staying here until Friday. is the unmarked, 'monotone' version – a simple statement of fact.

We are staying here, until Friday.

We are staying here – until Friday.

We are staying here. Until Friday.

progressively set off and increasingly emphasise the temporal adverbial.

Setting off a temporal modifier starting with 'until' after a negative statement gives an improbable dramatic change of direction to the sentence – a device that would only be used for such a dramatic effect.

I will not be firing any employees. Until Friday.