early 13c., probably from Old Norse skrapa "to scrape, erase," from Proto-Germanic *skrapojan (cf. Old English scrapian "to scrape," Dutch schrapen, German schrappen), from PIE *skerb-, extension of root *(s)ker- "to cut" (see shear (v.)).
Meaning "gather by great effort, collect with difficulty" is from 1540s. Related: Scraped; scraping. To scrape the bottom of the barrel in figurative sense is from 1942, in reference to U.S. employers facing worker shortages during the war.
mid-15c., "a scraping instrument;" late 15c., "act of scraping or scratching," from scrape (v.). Meaning "a shave" is slang from 1859. Meaning "embarrassing or awkward predicament" is recorded from 1709, as OED suggests, "probably from the notion of being 'scraped' in going through a narrow passage."
To get, esp laboriously and bit by bit: Dollar by dollar they scraped up a million/ even if you can't scratch up all of that cash now (first form 1617+, variant 1922+)