3% is a low-end estimate for Spanish flu. And look at how little the modern person even thinks of it. It's pretty impressive the level of death that can be swept under the rug of history. Accounts from the day report that there was a strange sort of refusal to accept Spanish flu at the time (probably helped by the vast conspiracy of silence due to political manipulation of the press during WWI), and as soon as ten years later people had basically put it out of mind.
As for populations reaching a limit, the curve you are looking for goes a bit a like this (presumably eventually leveling off the match the logarithmic population curve of a population living efficiently within its capacity):
The reason that current population growth does not already look like that is due to continued scientific advancement (most notably advancements in nitrogen fixation developed during WWI).
Are we heading for a dieback? Almost certainly yes. But it is by no means guaranteed. We adapt to our situations quite well through technology, we always have. And even if we don't, while the moral tragedy of the loss of that many individual human lives is staggering, we will adapt to the situation the old fashioned way through selection. Regardless, the species is not at great risk and I wonder if there would even be a great or sustained reaction to such an event.
Emerging infectious diseases are a greater concern, but the worst case scenario is 97% mortality (a figure derived from the failed extermination attempt of Australian rabbits). Again, enough to destroy all of society as we know it, but humanity itself may yet prevail.