I believe that widespread public understanding and support of longevity science is a necessary step towards a large and well-funded scientific community focused on achieving engineered longevity. On longer timescales (a decade, a generation), resources for research and development most reliably flow towards the areas of greatest public knowledge, desire, and approval. Just look at the many, many projects that have long been technically possible yet not been accomplished in the past decades: the creation of an orbital flight industry, for example, colonizing the sea, or irrigating the Sahara. Engineering the reversal of aging is a large and multi-faceted project that will run over a generation or more, even once the research community is fully engaged and progress is well underway. Ergo, public support is needed.
But let's play devil's advocate for today. The people who will be performing the necessary work to repair and reverse aging are life scientists and the halo of technicians surrounding that core research community. Those scientists also set the stage for the range of projects likely to be approved by funding organizations through education (both direct and indirect), the nature of their grant proposals, and so forth: they are the arbiters of truth when it comes to what is possible.
We are fortunate enough to still live in a society where the output of the scientific process is generally regarded as the truth. (Not that the output is always viewed favorably, lacking factions, or easily interpreted, but it does have a weight of respect rarely found elsewhere). So, the argument goes, if you persuade a significant community of life scientists to talk about and be interested in working on aspects of engineered longevity, everyone outside the scientific community will come around to support that work. In this way of looking at things, the scientific community is the seed for bootstrapping widespread support for extending healthy life and widespread understanding of the potential methods of doing so. Start with the scientists and others will follow.