Again, the problem is that of a combination of things.
1) you need at LEAST 500 unrelated individuals of a species to have even a hope of a viable gene pool (see also, "why are cheetahs endangered?") Over 1000 for a reasonably good chance at long term survival.
2) Neanderthal skeletons are old. Very old. The DNA in those skeletons is contaminated with fungi, bacteria, and is degraded terribly. It takes a great deal of effort to sequence a single genotype from a quality specimen. A good deal of that is spent laboriously piecing together the fragments of the broken down DNA from the sample, and ensuring that it is not contaminated by any of the prior contaminants, nor with human lab technician DNA. This is a very difficult and currently still very costly process. (but the cost IS going down!)
3) There are only so many places where neanderthals are known to have had persistent range of habitation, and where remains are likely to have been preserved. This makes finding the remains difficult to begin with.
4) There is a general lack of funding for general sciences, of which field biology of extinct species like neanderthal is one. This means that even if remains were more plentiful, there would be great difficulty procuring sufficient numbers of quality remains to sequence.
5) There is a strong "Dont play god!!" and "Think about the HUMAN babies before you go making copies of extinct non-humans!" demographic that would be **VERY** vocal against such a project, (because they are fucking idiots and bigots besides)
All of which would actively thwart any such project. Throwing a single very gifted or skilled scientist at the problem wont fix any of the above. About the only tractible one would be the funding one. I think we can all agree how fruitless a campaign to increase science spending would be, because of how terrible special interests are in politics, and the low ROI of academia in general. (EG, we have too many economists in govt, and not enough philosophy or science grads- which is a pretty good reason why we have the kinds of social disorders we have today. EVERY FUCKING THING boils down to "Will it make *insert here* fucking fabulously rich?" with the answer to that question being what drives whether a project will get funding or not.)
Still, I am with Rolan about the clear benefits of cloning neanderthal. The difference of opinion they would bring to the table, because of their differently wired (but equally valid) neurology would be very valuable to us as a species. To me, that alone would justify their resurrection, but many, MANY people would disagree.