There are both scientific hurdles and ethical concerns that need to be addressed.
Someone else can probably expand on this more, but the most interesting conversation I've seen in the ethical debate is 'where are they going to go?' Basically, what reason are we doing this for? Are we just bringing back a wooly mammoth-like animal so that we can say that we did it? Are we doing it as a prototype to see how far back we can recover an extinct animal from? Or are we trying to someone re-establish wooly mammoths into a habitat in the wild?
I think that the first two options are of limited scientific utility, and the last option is of some ethical utility if you highly value up-front biodiversity. However, introduction of the wooly mammoth into pretty much any habitat would shock the ecosystem (they are, at this point, invasive species).
There are something in the neighborhood of 1.5 million nucleotide differences between wooly mammoths and asian elephants (not all of these will be phenotypically significant!). In Jurassic Park, they sort of glossed over the 'putting together the dinosaur genome' part. Realistically, you can't just print out chunks of custom designed DNA and paste them together into a full animal genome, the genomes are just too big. George Church's group has instead been using CRISPR to introduce changes to genes that they think will result in noticeable phenotypic changes. Once you've introduced enough of those changes, then you're probably ready to try to start IVF work.
Somatic cell nuclear transfer has not been successfully performed on elephants (we haven't cloned elephants yet), so it would take some years to work out the kinks in that (generally, each species requires extra legwork to get cloning to be viable). So we are still years away from being able to actually get something that resembles a wooly mammoth born.