This is a **very key issue,* and like all such issues has many facets. People in general have a fear of the unknown (often with good reason) and also fear exploitation of things they care about by powerful, uncontrollable interests (also often with good reason). Synthetic biology still has a fairly low profile, so it's unlikely in the very near future to trigger a reaction such as that surrounding the early days of genetic engineering with the Asilomar conference and actions by city governments in Berkeley, CA and Cambridge, MA to impose moratoriums on research involving "recombinant DNA." Nevertheless, strident protests akin to those from that time 30 years ago or to the more recent objections in Europe to GM crops might well emerge, especially if something untoward happens in the course of a project that is labeled "Synthetic Biology." Such protests could seriously damage SB as a field, either by forcing premature, heavy-handed regulations on the laboratories that do SB research, or curtailment of public funding for such research.
In this area, the key operative word that describes the public susceptibility to a damagingly negative reaction is "unknown." As Markus has noted, publicity for successful, positive SB projects that clearly benefit humanity (e.g., Jay Keasling's work on biosynthesis of artemisinic acid in fermentation cultures) will help mitigate this problem of public ignorance. So too, I believe, do the iGEM competitions. It's an amazing experience to attend (as I have for the past two years) the annual iGEM jamboree. Even watching it on the web gives an idea of how enthusiastic the iGEM participants are after only a summer of work in an area that most of them knew little or nothing about beforehand (see
http://2008.igem.org/Previous_iGEM_Competitions).
Beyond the "poster-child" projects and iGEM lies the much more difficult task of improving the public's scientific literacy in the areas of molecular and cellular biology. In the US a large proportion of the so-called "educated" public remains woefully ignorant of even the most rudimentary facts about gene expression, cellular metabolism, etc. If a technology like SB is to find a welcome reception in society it needs to have a prepared public...
Finally, I think it's important to temper the hyperbole with which SB is often described. No technology ever gets off the ground as swiftly as its backers usually promise, nor does it necessarily hit its stride as a major contributor to the health and welfare of society as quickly -- or even in the projected manner -- as the backers initially assume. Thus what might have aroused a very positive initial public perception can turn sour if it fails to deliver on its promises, and the inevitable critics can capitalize on every small mis-step to denigrate the field. Better to understate the potential benefits and then roll out a pleasant surprise.