Xinhua词典: 方言, lit. 'no door / no way in', i.e. no pathway to getting it done. Snappy Beijing flat-rejection that's crossed fully into nationwide casual speech. More emphatic than 不行 or 不可能.
memory
Visualize the 门儿 (door) slamming: no door = no entry = no chance. The erhua 儿 on 门 is obligatory — without it (没门) it literally just means 'no door' and loses the idiomatic force.
