Did you check amazon's search inside for Miss Manners' books?

I love this phrase. It has helped me so much, especially lately.
Even if they ask "Why?"
Well, it just isn't possible. (With the implied, "None of your business and aren't you rude for asking" attitude.)
If they press further, they are A-holes.

I kind of treat it like "It's beyond my control," from Dangerous Liaisons.
Or, "It is what is it is."

I wish I had a cite for you, but as a person who has had boundary problems in the past, I can tell you it's a gem.

Huh, I'll have to give that a shot with my folks, but likely they'll get pissy and think I'm being uppity/rude/ungrateful/bitchass/etc.

I'll look tonight in my big blue Miss Manners' book; I'm sure it or something like it is in there.

It looks like it comes from this forum, Etiquette Hell.

The "I'm so sorry, it's impossible" excuse appears as one of a series of options in Miss Manners escalating arsenal of polite refusals, along with the False Excuse and the Lame Excuse. As she points out, "an invitation is not a summons."

Page 428, Miss Manners' guide to the turn-of-the-millenium by Judith Martin:

In these cases, she believes in No Excuse. "I'm terribly sorry, but that night is impossible for me" can mean that you had already planned to be making a public fool of yourself for all to see, so you have nothing (else) to be ashamed of if caught.

I'm positive that this advice predates the citation I'm about to give you, but I can't lay my hands on my Judith Martin books right now. TPS, mine is a big pink book! ENORMOUS. Can't believe I can't find it, considering how big it is and how small my apartment is!

Aha! Here it is: Miss Manners' guide to excruciatingly correct behavior, pg 117.

It's not specific to invitations, but also extends to requests of other kinds. The reader's question ends with "Is indirect communication more appropriate than direct communication in professional and personal relationships?"

Gentle Reader: In some societies, it is. Elaborate conventions exist to enable people to field or ignore a request so as to make clear that it has been refused -- while also conveying how much pain it costs to refuse.

We don't go in for that sort of subtlety; we pride ourselves on our frankness. Yet Miss Manners is amazed and touched that in a society that suffers from only-too-straightforward communication, often in the form of a raised finger, many people still feel that it is rude to refuse any request. Also, they think they have to supply an excuse, which will be led into a tangle of implausible lies.

So they hedge. As you have noticed, this causes more trouble to those who mistakenly think their requests have been granted, than if they were refused outright.

The polite way to refuse is to precede the denial with an apology but no excuse: "Oh, I'm terribly sorry, but I can't." "I'd love to, but I'm afraid it's impossible." "Unfortunately, I can't, but I hope you can find someone."

It is not more polite to say, "Well, sure, if I can finish up my other stuff and I don't have another assignment, only my stepson may be in town then and I'm having trouble with my car, so I don't know."

Miss Manners then gives an example in the next question: how to decline allowing a stranger to use one's cell phone.

Bravo!