noun
flood of visitors; barrage of guests
Describes a situation where many visitors arrive in a short period, often implying the host is overwhelmed. The 攻め part carries a nuance of being 'attacked' or 'besieged' by guests.
See also: 攻め (せめ)
年末は来客攻めで、ゆっくり休めなかった。
At the end of the year, I was flooded with visitors and couldn't rest properly.
新居に引っ越したら、友人たちの来客攻めにあった。
When I moved into my new place, I was besieged by visiting friends.
攻め means 'attack' or 'offensive'. In compounds like 来客攻め, it figuratively describes being 'attacked' by something in large quantities.
Compound of 来客 (visitor) and 攻め (attack), literally 'visitor attack'. The figurative use of 攻め to mean a flood or barrage is seen in other compounds like 質問攻め (barrage of questions).