During Spring Festival, guests poured into his home faster than he could receive them.
Tips
history
From 《世说新语·言语》 (Liu Yiqing, Southern Dynasties): 从山阴道上行,山川自相应发,使人应接不暇 — 'walking along the Shanyin road, the mountains and streams come at you in such variety that one cannot keep up.' Originally about overwhelming beauty.
usage
Can describe positive (beautiful scenery, delicious dishes, guests) or slightly burdensome (work, messages) overload. 暇 means 'leisure/free time' — literally 'no time to respond'.