Many different rail lines were built in the western United States from the 1850s onwards. Was construction ever delayed/canceled due to difficulty in finding workers, or due to workers leaving the job?
I was surprised to find out that, yes there were troubles with labor shortages. From Public Broadcasting Station "American Experience" article on the "Workers of the Central Pacific Railroad",
I'd recommend either purchasing the DVD the series has on the transcontinental railroad, finding it at your local library, or at least reading the article. I imagine that given your interest in the subject you would really appreciate it.
There were absolutely labor crunches while building the transcontinental railroads--these roads were stretching across a vast, unpopulated (by European Americans, that is) and harsh terrain. Labor shortages were worst during the Civil War, for obvious reasons. However, I can't find evidence of any major delays in the railroads' construction. This is due in part to governmental support to the railroads, but I believe it is mainly attributable to the unique vulnerability of the Chinese laborers.
Irish immigrants were the other major labor pool available to the railroads, but they proved to be more "rambunctious" than the Chinese. Speaking English and facing less ethnic hostility than the Chinese (though still facing considerable hostility), they had better alternative employment opportunities. Furthermore, they looked more like your average American, and so could escape their labor contracts and blend into the surrounding population. Thus in the classic formulation of Exit, Voice, and Loyalty, Irish laborers had "exit" open to them.
But the Chinese were structurally more predisposed to choose "loyalty" to the railroad company than were other ethnic groups. "Exit" could result in imprisonment or worse:
"Exit" was even less attractive when construction teams were working in wildernesses miles away from Chinese communities. Such distance and isolation made "voice" a poor option as well. Chinese laborers on the Central Pacific maintained a strike for about a week, but it was destined to fail. Remember, construction crews were like moving cities, and so all food and supplies was delivered to these crews along the single track stretching back to its point of origin. In other words, the railroad company controlled the food supply.
When the Civil War ended, the bargaining position of the Chinese became even weaker. The Central Pacific considered applying to the Freedman's Bureau in order to employ former slaves on the construction crews. As one Central associate noted, "A Negro labor force would tend to keep the Chinese steady, as the Chinese have kept the Irishmen quiet" (Brands, 60-61).
In short, neither exit nor voice were attractive options for Chinese railroad workers. By default, "loyalty" ensured the timely construction of the transcontinentals. American Indians were more threatening than labor problems: Sioux and Cheyenne warriors made regular raids against the Union Pacific in spring 1867, destroying equipment and sometimes killing workers. As one railroad man wrote to Ulysses S. Grant at the war department: "We've got to clean the damn Indians out or give up building the Union Pacific Railroad" (Brands, 65).