How long the deadline is depends on your buffer size and sample rate. To my ear, buffer sizes of >128 samples (at a sample rate of 44.1 KHz) have detectable latency (although the amount of latency will depend also on how many applications are in your signal chain). At 128 samples you have just under 3ms to do your processing.
Also note that for graphics, the output is the GPU itself. So you don't need to wait for the output to move back to the CPU, it's already where it needs to be.