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)
At the end of the year, I was flooded with visitors and couldn't rest properly.
When I moved into my new place, I was besieged by visiting friends.
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).