Curses, you have beaten me to it, I had been meaning to make a post about this for some time.
There are a lot of factors to take into account for a situation like this, such as increasing rate of teen and unwanted pregnancies, falling health standards, increased numbers of people living to extreme old age, couples who have multiple children, falling fossil fuel resources, shrinking biodiversity, balance of living space to cultivatable land, increased rates of genetic diseases due to larger population, (to quote Mordin Solus "too much intel!"). Taken at face value and todays' current laws and regulations, a miracle cure drug looks to have one of two possible outcomes.
If the human race kept it's current rate of reproduction, then the strain on planetary resources would become phenomenal. Assuming the drug was cheap enough to export to Third World countries, that would result in a phenomenal population boom, as families in deprived countries are used to having multiple children, but many of these children die, usually from water borne infections. If all these children were suddenly to survive, this would be more than enough to counteract people in First World countries choosing not to have children or the displacement of the homosexual community. Added to illegitimate births and couples who choose to have multiple offspring, all of whom would have an increased chance of living to old age, the resultant population increase could crush a lot of the remaining biodiversity out of the planet, as humanity started looking for fresh land for building and farming, exploiting resources in areas previously overlooked. There could be the possibility of us, quite literally, wiping out the world.
On the other hand, if a population cap was to be brought into effect, then it could result differently. For arguments sake, let's say at the moment, 3 people in a thousand live to the age of 100. A cure-all could up that to maybe 15 in a thousand. That might not sound a huge increase, but replicated across the 6.9 billion people in the world it would lead to a staggering O.A.P heavy society, if less people chose to have children but lived to older ages, there wouldn't be enough "fresh blood" so to speak to provide necessary care industries AND persue technological advancements.
As such, a drug with the cure for all diseases could precipitate a population crash in the human race, one we would probably then recover from, but it would then most likely result large areas of cities becoming unoccupied, as people would still be needed to produce food and so would need to transfer to the countryside.
Personally, I think the best option in this scenario would be the development of interplanetary travel and widely available hydrogen fuel options. This would reduce strain on the planet and natural resources, allow a resultant increase in natural biodiversity, and facilitate the next stage in humanities evolution.
By the way, there's an internet site I found during a web trawl called Breathing Earth, sthowing the Birth rates, Death rates and fuel consumption of the entire human race. It helps put this sort of thing into perspective, if anyone's interested, I'll add a link.
http://breathingearth.net/
The Unworthy Gentleman said:
Oh, looks like we're hitting Malthusianism again.
Guess what - this was an issue years ago and we made it through fine. The population has always been rising and people have always said we're going to overpopulate the planet, run out of space and not have enough resources to survive. We made it through all those times with scientific and technological advances and we will time after time.
We used to build on the ground. When the time comes that we can't (or shouldn't) do that anymore then we'll build into the ground and into the sky. We've already started building to the sky, we'll have plenty of space for plenty of time yet. If we have the technology to cure every disease then we'll have the technology to mass produce artificial nutritional food as well. There is no problem here.
The population years ago (I'm not precisely sure what time scale you meant, so for the sake of argument I'll use forty years ago) was around 3.5 billion. World population today is tipping the scales at 6.9 billion people. That's almost double the number of humans living off the same amount of land, and scientific and technological breakthroughs aren't catching up fast enough, or in the cases of things like GM crops, are meeting up against ethical barriers. Building into the sky is all well and good, but when we can't build any higher we will continue to spread out, and a patch of land which before the advent of skyscrapers needed enough land to provide food for say 10 people, at most, that same building plot can now hold hundreds of people, but we can't yet provide the same sort of hot-housing for food, at least not on a large enough scale.
Your statement seems to assume that the solution will always in quick succession to the problem. I know necessity is the mother of invention, but this can sometimes take years, we've still not hit upon a viable replacement for fossil fuels yet, and (refering back to the OP) if a "miracle medicine" were to be discovered, the strain on planetary infrastructure and resources would be increased further.