Two years before Earhart's flight, several students and graduates of the Kamehameha School of Hawaii colonized the island as part of a research job. According to the Pacific Islands Benthic Habitat Mapping Center, of the University of Hawaii at Manoa, "The Kamehameha colonists constructed three runways on Howland using WPA (Works Progress Administration) funds as a possible re-fueling station for trans-Pacific flights and for use as a landing site by Amelia Earhart and Fred Noonan on their round-the-world flight in 1937" (see Pacific Remote Island Area (PRIA)).
According to Earhart researcher Ric Gillespie, Earhart's flight accelerated the construction of the landing field:
"On Thursday, January 7 , the White House received a Western Union telegram from Amelia Earhart in Burbank, California, addressed to ‘Honorable Franklin D. Roosevelt.’...'I hope to land on tiny Howland Island where the government is about to establish an emergency field...Construction party with equipment due to sail from Honolulu next week. Am now informed apparently some question regarding WPA appropriation in amount [of] $3,000 which covers all costs other than those born[e] by me for this mid-Pacific pioneer landing field which [will be] permanently useful and valuable aeronautically and nationally…Under circumstances could you expedite, as immediate action vital…Please forgive this troublesome female flyer for whom this Howland project is key to world flight attempt.'" The project was approved a few days later and the three landing fields were collectively called "Kamakaiwi Field," in honor of one of the colonists. (From Ric Gillespie, Finding Amelia: The True Story of the Earhart Disappearance, Annapolis, MD: U.S. Naval Institute Press, 2006, pp. 8-18)
The landing fields are mostly gone, but a 2008 photo of the remnants can be seen here: https://www.flickr.com/photos/72923065@N00/3380880233/.
Kamakaiwi Field is probably the most remote New Deal funded project. The $3,000 in WPA funding contributed to it equals about $49,000 in today's dollars.