I've heard a claim that the construction project proves that capitalism works and private industry is the best way to build things. However from what I've read the project pilfered huge amounts of extra money/land from the federal government and was fairly inefficient. What did economists or other public figures at the time think of it?
It was far more of a government orchestrated endeavor than purely a victory for free market capitalism.
The government sponsored Pacific Railroad Surveys before the Civil War but the different factions of the country couldn't determine the best route to take.
The government legislated Pacific Railroad Acts in 1863, 1864, 1865, AND in 1866 (if I recall correctly).
The government provided US Army engineers. The government also backed bonds and put them up for sale in an effort to raise money needed for construction.
To entice railroads further, they promised them the land surrounding the track routes to be sold off to the highest bidder.
Ultimately, three private companies are credited with building the railroad itself. Sure. But it simply wouldn't have been possible without the funding, land, surveying, and permission granted by the federal government. If anyone tries to convince you the earliest transcontinental railroads were "triumphs for free market capitalism," they are extremely ignorant of the actual history of this country.