A class for remember me
From a once over:


You are a bit overdoing the blank lines in your definition of A
I like the namespace idea, given how you implement getObj and setObj, it would be nice if the caller could set the namespace.
setType -> I get that remember probably means you want to remember info across sessions, hence you choose localStorage and not sessionStorage, still something like persist or persistAcrossSessions could be more informative.
setObj -> does totally not what I would expect it to do, I would expect your code to JSON.stringify() and assign that to a key, however you store each property individually which can make for a very messy retrieval
getObj -> does exactly what I thought i would, give all properties in 1 object, this is very limited functionality. You should consider really consider JSON in your class.
clear -> I would make var key part of the for loop : for (var key in this.A.storage) {
Commenting is uneven, the 2 functions which are most surprising to me have no comments.