[susan53]

Well yes - you can if you're able to time travel and find yourself in the 13th century. But I wouldn't try it in the 21st in the way you're talking about. You'd change the meaning. In that position "not" negates the infinitive - the sentence would mean "it's necessary that you don't do XXX" - which is rarely used. But compare eg :

I don't like getting up early.
I like not having to get up early.

To understand these sentence you have to chunk them differently depending on the scope of the negative particle :

I don't like / getting up early.
I like / not having to get up early.

With "need" I could see it happening in some sort of counselling or psychotherapy session:

I need you not to keep nagging me. = It's necessary for me that you stop nagging

But the meaning differs from

I don't need you to keep nagging me = It's not necessary for you to nag me.

which can also be expressed modally : You needn't keep nagging me.