Construct: X都不X一下, Mandarin? I've come across the following construct recently:

X 都不 X 一下

Specifically what I heard was:

痒都不痒一下

(Bonus points to anyone who knows where that comes from...)

Is this a mandarin construct?

Can X be replaced with any verb?
Yes, that's fairly normal. In fact the actual construct here is merely ... 都不 .... 

It is somewhat more commonly seen with the character 連 ("even") prefixed, i.e. 连痒都不痒一下. Similarly, the counter 一下 ("once") at the end is optional, i.e. 痒都不痒. All three forms express the same meaning of "not even once / not at all".

Taking all three into account: (optional: 連) [verb] 都不 [same verb] (optional: [single counter for action])

Note that the counter does NOT have to be 一下. So while any number of verbs can be used with this construct way, you should take note to use the appropriate counter for the action. Or alternatively, don't use any at all. Examples:


連吃都不吃一口: S/he/they wouldn't even take one bite (一口, lit. "one mouthful").
連看都不看一眼: S/he/they wouldn't even look once (一眼, "one look").
想都不想: Without thinking.