Just a note here: Having mechanical issues with your vehicle (your private property) does not give you the right to break driving laws. A car with a flat is still capable of driving enough to move out of the way to a space that isn’t impeding traffic and/or putting others in danger.

Granted, blocking a bike lane isn’t likely to put someone in immediate danger, but you are still blocking people from getting past so some amount of anger should be expected. Cyclists have to deal with so much crap being parked/dumped/littered in their bike lanes.