The phrase “to put one’s shoulder to the wheel” means: To assist with might and main; to labor vigorously in behalf of a cause, project, etc.
In the physical sense one put one’s shoulder to the wheel to aid his horse in pulling a cart or other vehicle out of the mud or over an obstacle.
And when a horse required such aid, it was certain that vigorous effort was needed. No halfway measures are implied by the expression.
Figurative usage dates back to the seventeenth century, but I have no doubt that the captive Israelites under the Pharaohs of ancient Egypt were often obliged to perform the task literally in the building of the pyramids.