I have to start with a disclaimer: it depends from jurisdiction to jurisdiction, and I'm much more familiar with European and UK standards of obviousness.
The brief answer is that there has been precedent to suggest that identifying a technical problem to solved can itself be inventive. Put very broadly, something like "I want to make product X be better" isn't an objective technical problem to be solved, it's a desired outcome. But identifying a way in which to make product X better, followed by a means to implement it, may be non-obvious. The larger contribution in that case might well have been the identification of the problem, but that itself could have been inventive ("inventive" and "non-obvious" are used more or less interchangeably).
My favourite example is the Anywayup Cup (Google it - also a great example of how patents can be enormously beneficial to the little guy). Anyone who's had a child (I'm told!) knows that kids spilling juice is a problem. The Anywayup Cup is a sippy-cup which, essentially, has a valve flush with the sipping portion. If you framed that problem as "I want a way to stop liquid from leaking out of the apperture in a sippy-cup" then that's an obvious solution. But that wasn't the objective technical problem to be solved; the problem to be solved was "I want a way to stop kids making a mess when drinking juice", and identifying the technical means to do so was the lion's part of the inventive step there.
(there was more to this particular case than that - for example, there's the "long-felt want" argument here, because kids making an unholy mess with juice isn't exactly a new problem, so why hadn't a solution been presented before? This is not enough to demonstrate inventiveness, but it may contribute depending on the circumstances.)
Both the UK and the European Patent Offices have pseudo-objective tests for assessing obviousness - the Pozzoli/Windsurfing test and the Problem and Solution approach, respectively. Common to both is ensuring that the problem to be solved is identified, the relevant skilled person is identified, and - arguably most importantly of all - the avoidance of hindsight. Nearly everything's obvious in hindsight.