The expression “at the eleventh hour” means with not a moment to spare; at the latest time possible; just under the wire.
This is of Biblical origin, Matthew xx, 1-16: “For the kingdom of heaven is like unto a householder, which went out early in the morning to hire labourers into his vineyard.
And when he had agreed with the labourers for a penny a day, he sent them into his vineyard. And about the eleventh hour he went out and found others standing idle, and saith unto them, Why stand ye here all the day idle?
They say unto him, Because no man hath hired us. He saith unto them, Go ye also into the vineyard; and whatsoever is right, that shall ye receive.”
But at evening all received the same payment. Despite the protests of those who had “borne the burden and heat of the day,” those who came at the eleventh hour received a penny, just as those who had come early in the morning.