When North Americans built the railroads in the 19th century, they did not let the mountains, rivers, and forests stand in their way. No, sirree. The speed at which the rails were laid and the disregard for obstacles in their way inspired the expression "to railroad" as early as the 1870s. Its figurative meaning grew over time: First it meant to send a person to jail without a fair trial (and pretty hastily, too).
More recently, the expression has come to mean rushing important legislation through Congress and bypassing various procedures and formalities.
This word for rapid or fast originally had nothing to do with speed. It simply meant "living." Therefore, at one time livestock was called quickstock. Quicksilver, or mercury, was so named because the metallic element moved about freely as if it were alive - living silver! Quicksand, too, shifts its place as if it were living, and a living hedge of plants was called a quick fence in Old English.
Today, the soft, sensitive skin under a fingernail or toenail is still called the "quick," named for its tender tissue. And figuratively, "to cut someone to the quick" alludes to tenderness and sensitivity, as in hurting what is innermost - one's feelings.
SOURCES: 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; 'Brewer's Dictionary of Phrase and Fable,' by Ivor Evans; 'The Barnhart Dictionary of Etymology,' by Robert Barnhart.