Does the phrase “don't even pass the laugh test” pass as an idiomatic expression, or only a set of words?

Summarising and amplifying the comments thus far, the earliest usage I can find is a 1985 Supreme Court usage...

The Supreme Court said, “This doesn't pass the laugh test; not withstanding what the Ninth Circuit says, we are not going to require that a recipient receive notice of every subpoena that has been issued in the investigation.”

For several years after that, almost all instances in Google Books seem to be in legal contexts. Interestingly, the straight face test predates it by several decades (that link has one from 1956).

In practice it does effectively mean this is laughable. Given the origins are so clearly associated with legal circles, I prefer to see it as implying this would be laughed out of court (if it ever got that far). But as StoneyB says, you can also see it as so laughable you couldn't say it with a straight face.

Any strong dismissal of someone else's point is bound to be "offensive", but arguably this particular one introduces a touch of self-referential levity (from the point of view of third-party onlookers, not the person whose position is being so derisively "laughed off").

Anyway, over 3000 written instances of pass the laugh test show that it's not at all uncommon.

To take your points one by one:

• it is not an idiom (it doesn't mean something other than what it says

• but it is a pattern (more technically a 'snowclone') or

doesn't pass the X test

with 'even' has the nuance "consider how it might help the terrorists...it doesn't at all; the suggestion could be laughable but is so so much unhelpful that it is not even laughable, it is just boringly wrong" (That is my interpretation of the words, not mu understand of the situation).

• Yes, you could say " “Your idea (invention / rhetoric / logic) doesn’t even pass the laugh test” and that would be pretty dismissive, because the implication is that the idea is stupid.

• 'laugh test' is a fairly new composition and not a set phrase or idiomatic at all.