One day on planet Earth, for reasons that are not immediately apparent to the population, all natural sources of oxygen production stop producing oxygen. No new oxygen is output from any natural source, whether it be on land, from the oceans or elsewhere.
How long would it take for:
All the info we need to calculate this is in the wiki for the oxygen cycle. The atmosphere gains and loses about the same amount of oxygen each year: 3 $\times$ 1014 kg. It also currently holds 1.087 $\times$ 1018 kg (34 $\times$ 1018 mol converted to kg).
So we could, back of napkin, last 3,000 years. In reality we would either die much earlier because not even sherpas could breath in an atmosphere with 60% reduced oxygen concentration (at sea level, effects would be deadlier at higher altitudes), or survive much longer because 3,000 years is way enough time to come up with some technology to allow us to survive at least in bunkers.
By the way, scientists would notice this really quickly. Plants in labs would act weird around the world (there are many labs experimenting with photosynthesis, you know). You would also have massive acidification of lakes and oceans right away, since all that phytoplankton stopping producing oxygen would be almost equivalent to all of it dying suddenly. They are the major source of O2 for surface water, since atmospheric oxygen takes longer to diffuse into water than plankton takes to replenish it.
So... this might make major news within a day or two.
Most probable scenario: scientists warn about the end of the civilized world within the century, deniers claim it's a conspiracy theory to plant microchips in everybody through vaccines (the less sense it makes, the more they love it). Politicians argue in circles about what to do for decades without any practical actions taken. 100 years later historians are discussing about a time when people lived outside bunkers. But the average, future bunker citizens think that's a plot to socialize oxygen, which they won't allow.
The limiting factor on survival would be food. No photosynthesis = no plant growth = no new food. The world very soon turns into the Rwandan genocide + cannibalism. Even with full recovery of the bodies you're looking at about 3 years before the world is reduced to bacteria.
It's not the lack of oxygen so much as the accumulation of CO2 that we would notice first. And that would happen far sooner than we would notice the lack of oxygen, per se. (I'm addressing when the average human would experience a difference in daily life, not whether scientists would notice the atmosphere changing, something that would take very little time.)
Today, atmospheric CO2 is around 0.04% worldwide. If plants stop synthesizing CO2 into glucose (photosynthesis) and the atmospheric CO2 level rises to just 0.5%, we would notice its effect on our daily routine almost immediately.
For example, at 0.5% ambient CO2, astronauts on the ISS "experienced headaches, lethargy, mental slowness, emotional irritation, and sleep disruption" (source). At 1% CO2, we would notice our bodies reflexively trying to breathe better. We can survive CO2 levels between 1% and 2% for only about one month. We would survive for 1 week at 3.5%, and 8 hours at 4.5%. Medically, the resulting condition of too much carbon dioxide in the blood is called hypercapnia. I understand that this occurs because CO2 does not leave our bloodstream efficiently when the partial pressure of CO2 in our lungs is too high. (Chemists, feel free to correct me.)
How long would this take? A rough calculation:
Mass of atmospheric O2: 1.4 × 1018 kg O2 (Table 1)
Mass of atmospheric CO2: 1.4 × 1018 x (0.04/20.9) x (44/32) = 3.7 x 1015 kg CO2
[The line above converts current O2 mass to current CO2 mass via two ratios: their relative % of the atmosphere, and their relative molar masses.]
Annual oxygen production: 3 x 1014 kg O2 (Table 2)
One year of respirated CO2 not converted back to O2 via photosynthesis: 3 x 1014 kg O2 x (44/32) = 4.1 x 1014 kg CO2. (This is the annual increase in CO2 if there is no natural production of oxygen.)
CO2 is now 0.04% of the atmosphere. It needs to grow by a factor of 12.5x to reach 0.5%, by which point we would certainly feel the effects (see ISS astronauts above).
This requires adding 11.5 x 3.7 x 1015 = 4.25 x 1016 kg CO2 in total.
At an increase of 4.1 x 1014 kg/yr CO2, this would take 104 years.
Short answer: We would all suffer "headaches, lethargy, mental slowness, emotional irritation, and sleep disruption" no later than 104 years from now. In reality, people already experience these things after a couple of hours in closed bedrooms, offices, and meeting rooms with poor ventilation, as ambient CO2 increases, so such problems would become commonplace far sooner than a century.
So without technological intervention (say, reducing CO2 levels indoors), we would suffer serious effects even with abundant oxygen all around us.
It would be analogous to floating in a lifeboat in the middle of the Pacific: "Water, water everywhere, and not a drop to drink."
I'd like to offer a different approach to your question, which was already briefly mentioned (as in this answer and this comment): oxygen, more accurately molecular oxygen (O2) is not a "purposeful" product made by plants, algae or bacteria. Quite the opposite, molecular oxygen is a by-product of the reduction of CO2, and by the way a very toxic by-product, which the autotrophic organism needs to get rid of as soon as possible.
In short, this is the reaction:
The protons and electrons are used to reduce the CO2, allowing the production of organic compounds, and the O2 is quickly discarded (or itself reduced, e.g. respiration).
All that being said, the real question becomes:
If all natural production of organic compounds1 stop, how long do we have?
That, I'm afraid, will have consequences much deeper and faster than the depletion of atmospheric oxygen (which may take longer before it starts affecting aerobic organisms) or the increase in atmospheric CO2. Lack of organic compounds, aka food, is the main issue here. Just think about the sun disappearing: no more light, no more reduction of CO2, no more food. It's roughly the same scenario.
1 There are other biochemical pathways for reducing the CO2 without oxidising water, but they are negligible.
- Humans to notice that no new oxygen is being output?
Immediately they notice all the plantlife is dead. The only way all plants would stop producing oxygen is if they're dead, it's not a choice they make, it's a necessary biological function.
- Earth to no longer become livable for humans/other typical Earth life?
Shortly after 1) when the nuclear holocaust starts after they find out all the plant life is dead.
Photosynthesis is the bedrock upon which almost all life on this planet ultimately depends. No photosynthesis means no phytoplankton or plants, and no phytoplankton or plants cuts the bottom out from under the food web. Herbivores and their aquatic equivalents quickly starve as their food all dies, and then the predators of those herbivores starve, etc., until what's left are mostly carrion eaters and other decomposers like fungi, bacteria, etc. And eventually even those will eat their way through all of the other once-living matter and die themselves, leaving the world covered in nutrient-rich but lifeless dirt.
The only survivors would be a few pockets of life based on chemoautotrophs at places like deep-sea vents, which get their energy from breaking down chemicals like hydrogen sulfide or ammonia. Theoretically they could eventually expand out into the rest of the world, but given the extreme conditions that most chemoautotrophs require, it's unlikely that they'd be able to spread far from their specialized energy sources.
Humans might muddle along for a while relying on stored food, but unless there's a major breakthrough in turning waste and raw nutrients back into food on a massive scale in a way that doesn't involve plants at any step, we are eventually going to run out of food and die.
When deoxyhemoglobin picks up oxygen, that's a chemical reaction (forming oxyhemoglobin). When oxyhemoglobin releases oxygen, that's a chemical reaction too (forming deoxyhemoglobin plus oxygen), and that seems to me that it's no less a "production" of oxygen than photosynthesis. So it seems to me that the answer is that we would all die very, very quickly.
