How strict are paper revision deadlines?
The strictness of the deadline strongly depends on the journal and the context of publication.  For most papers to most journals, there is potentially a great deal of flexibility (assuming that you ask early and are polite about it).  The main exceptions that I have encountered are:


High-impact journals sometimes expect you to drop everything else on their behalf, and thus may give both a short deadline and little flexibility.
Articles submitted for a special issue sometimes need to hit particular dates in a production schedule, and thus may not have much flexibility to give.