Actually, it should be trivial to tell that, before the first deadline, we already have 4ms of work and can't allocate another 4ms of work. I think the real issue is that, if you've got two tasks with slightly different periods, they may be fine for the first deadlines, but slowly drift into phase, at which point the processor is oversubscribed until they drift back out of phase.
Say you're doing video processing on a stream at 60 Hz and one at 50 Hz. If you've got tight windows between when the input is available and when the output is required (say 2ms of work out of 3ms of real time), you may be fine for the first 100ms and then have to do both frames at the same time. Or the streams might be staggered such that they never conflict.