I think this would probably work. The grandmother effect, which is one of the main theories for human longevity after fertility might indicate that human lifespan would increase if the children come later.
Just have to disclaim here: We will never do this. Many unthinkable consequences would result...
If you simply forbid anyone to have children before they are 40 or 45 (fertility doesn't drop until age 35 or so), forbid invitro fertilization and medical assistance to conception we would probably be looking at a prolonged lifespan. Infertility rates in women at age 40 are not clear, but one estimate is that 40% of women can have children at 40 years of age. If we want to seen an effect early, we would push the age up a year or two. Forbidding in vitro fertilization and other medical assistance to offspring we could look like a 80-90% cut of people - lots of people would never have children. This might make people unhappy an destabilize the social fabric.
Its not clear how long this would take. The generation time would go to 40 years from about 20 now - 40 to get to childbearing age, but results would take 80 years - when we find out how the children would fare. Given the C elegans longevity experiments and the fact that we are starting with 8 billion people, we probably would find some great late age breeders who may also live long. But for the longevity phenotype to set in it would take several generations as we are looking for an indirect effect: later breeding causing longevity. The Belyaev experiments which produced domesticated foxes by strong selective breeding took some 30ish generations to complete though they saw a significant effect in just 10. It could take a similar numbers of selection rounds in this cse. 4-500 years. Ethical issues aside, this is why most geneticists study flies.
There would also be a lot of other negative socioeconomic consequences to this thought experiment. One good thing is that the population of the earth would plummet - many people would be eliminated from the gene pool, though eldercare would be a major part of the world workforce. Lots of work, not clear who is going to pay for it, but low unemployment and low low wages may result.
So you see Mister President, this is quite a distinct possibility, though some sacrifices would have to be made.
The science of human eugenics is not scientifically wrong, but selective animal breeding and lab experiments don't usually evaluate or care about the consequences of large peturbations in the gene pool.
You would also have a lot more autism and Downs syndrome and other congenital defects which tend to show up in offspring of older parents. These issues might improve with application of biotechnology which screens weak sperm and eggs without ruining the effect you are looking for, maybe not.
Since we are selecting against fecundity, the human race could be dogged by fertility problems or chronic genetic diseases which the genetic contribution of some of the more robust people in the gene pool being removed and the tendency to such age-related birth defects might not go away given the drastic selection pressure we are putting on the gene pool.
Other consequences you might not expect; some physical traits associated with longevity and prolonged fertility would cause us to look more alike and not necessarily in a good way. Browse the internet; its probable that we would get shorter and possibly uglier?
There are many more direct ways to increase the human lifespan - better diet, exercise, the elimination of poverty, vaccinations, proper medical care, access to clean drinking water and a lower birth rate (fewer children not later) all are known to directly effect longevity, having more than doubled the human life expectancy in the past few hundred years.