Less than a day. There is a lot of human monitoring and intervention required to operate a large power grid successfully.

Let's take where I live for example, Ireland. Grid operators are aware of any major event that is taking place such as a World Cup Soccer match and would be waiting to release excess capacity into the grid when the half-time whistle sounds to counteract people all across the country boiling their kettles at almost the same moment.

One way of managing this is pumped storage, where water is pumped up to a reservoir during low demand periods (usually during the night) and releasing the water through turbines to generate more power when required before pumping it back up to the reservoir but this has to be triggered by the grid operator.

What would happen if the grid operator didn't release extra capacity into the grid when required?

The supply frequency and voltage need to be carefully regulated as straying too far away from the nominal values will lead to a bad time. Imagine the grid is like a car engine with a manual transmission and the customer demand is like the road. When the engine power and gear selection matches your speed and road conditions, you travel along smoothly.

Now imagine you come to a steep hill (this is the extra demand on the grid), the driver (grid operator) should drop down to a lower gear and put their foot on the gas (extra capacity) to get up the hill smoothly but let's say the driver has fallen asleep. The engine (grid) will start to slow down as the hill (demand) becomes steeper. The engine will start to labour and eventually it will cut out.

This is an oversimplification of what would happen to the grid but it's not a million miles off. Without compensating for increased demand or reduced supply (if a generator trips offline) the voltage and frequency will start to drop off which causes the current to increase and this will trigger overloads on downstream circuits. Upstream, as the generation stations see the grid frequency and voltage fall, they might also trip offline to protect against damage from mismatched frequencies.

Lots of modern circuit breakers can be set to auto-close after a trip so the circuits would attempt to come back on but after another trip they might go into fail safe that can only be reset manually.

You might get large parts of a city or state going into blackout which might temporarily solve the extra demand issue as the load has been shed but, depending on how many generation stations tripped offline, you might already be into a cascading failure type situation where more and more generation stations trip offline until there's nothing left online.