The Spring Festival gala was so dazzling the audience couldn't keep up.
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history
Adapted from 《世说新语·言语》: Gu Kaizhi, traveling the Shanyin mountains, said 从山阴道上行,山川自相映发,使人应接不暇 — 'mountain after mountain reflects on each other so there's not time to take it all in.' 应接不暇 evolved into 目不暇接 when the emphasis shifted to the eye (目).
usage
Positive — the overload is pleasurable. Describes visual abundance: scenery, shop displays, gallery openings, light shows, performances. Natural with 让人, 令人, 使人 as a causative.