1/2 a day? It all depends on where you start.
Sea level -> 2,000 meter in 1/2 a day and stay there for an extended period: no problem
6,000 meter -> 8,000 meter in 1/2 a day and stay there for an extended period: You would not be a happy camper
Most people can handle 2,500 since that's what's simulated when you fly an airplane. Above that, people with physical conditions can get problems.
General rule of thumb is that it takes 1-3 days to acclimatize to a new altitude/less oxygen (we can speak in climbing terms since it's the same effect), the times depends on your physical condition. When you climb, you should not climb more than 300 meters and sleep there. If you climb more than that (like when they go for the summit), they climb during the day and sleep at the altitude they are acclimatized to.
The time it takes for a climber to get acclimatized to camp 4 at 8000m (where they start the summit climb from) from base camp at 5400m, takes about 1 month.
So climbers have definitely proved that the body will not adapt to change of oxygen in less than 1/2 a day.