Use of 'Let Alone That'

The idiomatic phrase "let alone" is roughly equivalent "much less" to "not to mention." Think of it as a kind of emphasis to further illustrate the speaker's point. For example: "We hadn't got the money to phone home, let alone stay in a hotel." In this case, staying in a hotel is not possible. How could they? They can't even afford to phone home!

Here are some more examples:

"We have no room for another house guest, let alone for an entire family!"

"We have no room for another house guest, not to mention room for an entire family!"

"We have no room for another house guest, much less for an entire family!"

Again, housing an additional family is out of the question. They can't even handle one more person.

We can break this down into something of an equation: A + idiomatic phrase + B, where B is emphasized over A (B > A).