Looking for an origin for "land office job"

Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013) has this entry for the seemingly closely related phrase "land-office business":

land-office business A thriving, expanding, or very profitable concern or volume of trade. For example, After the storm they did a land-office business in snow shovels and rock salt. This term, dating from the 1830s, alludes to the throng of applicants to government land offices through which Western lands [in the United States] were sold. It has been used for other booming business since the mid-1800s.

And Alan Metcalf & David Barnhart, America in So Many Words: Words That Have Shaped America (1997) has this note on the phrase:

As the westward spread of settlers became a wave and then a tidal wave, the eagerness to register land claims and the push to purchase land created crowds at land offices. So picturesque is the image that land-office business became a descriptive for brisk business. "A practical printer," said the New Orleans [Louisiana] Picayune in 1839, "could do a land-office business here." In 1875 the Chicago [Illinois] Tribune remarked, "The tap-rooms adjoining the polls were all open and doing a 'land-office' business." In Louisville [Kentucky] in 1887, the Courier-Journal reported, "The doughty burglar ... has been doing a land-office business the past few days."

Land offices in the old sense are gone, but land-office business continues doing a land-office business in out language today.

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Early examples of idiomatic use of 'land office business'

An Elephind search turns up this idiomatic instance of "land-office business" in an untitled item from the [Evansville, Indiana] Tri-Weekly Journal (January 1, 1848):

The Madison and Indianapolis papers are quarreling about which of the two places has succeeded in "squeezing" the most money out of the State Treasury. If we know anything about it both places have done a land-office business in that line.

And from "Great Whig Celebration at Niagara," in the [Indianapolis, Indiana] Daily State Sentinel (August 4, 1852), quoting "the regular correspondent of the Madison Banner":

Pick-pockets have done a land-office business to-day. Several western gentlemen have been relieved of every cent of their money. A number of arrests were made.

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Early examples of non-idiomatic use of 'land office job'

Searches for idiomatic use of "land office job" are complicated by the fact that many early instances of the phrase refer, literally, to employment in one or another capacity at a U.S. General Land Office—a number of which positions seem to have been widely viewed as sinecures or opportunities for corruption and self-enrichment for those appointed or elected to them. Thus, for example, the Seattle [Washington] Post-Intelligencer ran a story with this headline in its October 6, 1893 edition:

The M'Intosh Hoax: No Fat Land Office Job for the Anti-Tillicom

And from an untitled item in the Delta [Colorado] Independent (October 25, 1893):

Mr. Geo. P. Crist, son-in-law of Mr. Potter of the Ventral House, arrived in Delta last week. He was one of many who made the rush at the opening of the Cherokee Strip, and secured a town lot at Pond Creek. He is a Simon-pure Kansas Democrat, and has his eye on a land office job, as there are changes soon to be made in that new country.

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Examples of idiomatic use of 'land office job'

Although this background might suggest that idiomatic use of "a land office job" could be used to mean "a lucrative position requiring little effort," actual instances of usage hew much closer to those for the earlier "land use business." For example, from a letter written in Naples, Italy, by Helen McKee dated March 7, 1944, reprinted in Judy Litoff & ‎David Smith, We're in This War Too: World War II Letters from American Women in Uniform (1994):

We are still doing a land-office job on orthopedics and the Penicillium ward is going strong. The results are marvelous—most unlimited results. Can you imagine these grossly infected wounds, covering a large area, mostly with bone fragments protruding up into the wounds.We used Penicillium on some of these cases for a period of three days and found the wounds clean and healthy at the end of the third day period.

McKee was from San Antonio, Texas.

From "Homemaking—These Expert Tricks Will Make Worn Leather Bags Look New," in the Indianapolis [Indiana] Times (August 17, 1944):

Use the right kind of rejuvenating tricks on your old lather handbag and nine chances out of ten you can make it look as lustrous, supple and elegant as ever.

Brush your bag inside and out. Empty removable fittings. Plump out by stuffing with paper. Then do a spit-and-polish job on the outside.

These four steps, say the professional service people, doing a land-office job in bag restorations, will put all but the most battered bag back into the running.

From an unidentified issue of Esquire magazine, volume 22, part 2 (1944) [combined snippets]:

For Uniformed Gastronomes. A gourmet shop in Manhattan does a land office job in making up Christmas boxes for overseas gourmets. Each box might contain such things as paté de fois gras with truffles; lobster paste; oversize sardines, a smoked turkey or a whole boned chicken.

From a "Fighters Up-Again," in Air Force: Official Service Journal of the U.S. Army Air Forces (June 1949):

Field snack bar (above) was open during entire meet and did land office job.

From remarks by Senator Hoey of North Carolina on a resolution disapproving Reorganization Plan No, 1 of 1952 (March 12, 1952), in Congressional Record, volume 98—Part 2 (1952):

Furthermore, Mr. President, under the present law the President of the United States can remove a collector of internal revenue at any time he may wish to do so, without even one day's notice. However, if the collector of internal revenue were selected under the civil service system, then he would be in office, and it would be a “land office” job to remove him. In that case, regardless of the situation which might exist and regardless of everything else, it would be necessary to go through a long, involved process before the collector could be removed from office, even though he might be utterly inefficient and might be entirely lacking in the qualities and characteristics necessary for efficient service.

From "Salk Vaccine Administered to 293 Students of County: Work Goes Off in Hour with None Made Ill," in the Breckenridge [Texas] American (April 19, 1955):

Six Breckenridge physicians did a land office job with dispatch Monday in administering Salk vaccine to Breckenridge first and second graders, reports of County health officer Dr. Grover C. Wood revealed Tuesday.

And from Harry Marriott, Cariboo Cowboy (1966) [text not visible in snippet window]:

Our old stand-by, Uncle Bill, was really doing a land office job at the river, in growing us a pretty good supply of real good spuds, some fruit and a lot of sugar beets which were used to feed our hogs, brood sows mostly, in the winter time.

These are the only six relevant instances of the phrase that I found in a series of Google Books and Elephind searches. Five of the six cited instances—the three from 1944 and the ones from 1955 and 1966—use "land office job" to mean something like "brisk business" or "nonstop work." The possibly odd one at is Senator Hoey's from 1952, where the meaning seems to be something like "full-time job" but could be "extremely or unduly hard work"—and perhaps even something like "as difficult as ousting someone from employment as the General Land Office."

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Conclusions

I don't recall ever having encountered the idiomatic expression "land office job," which leads me to believe that it wasn't especially widely used in any of the parts of the United States where I've lived for more than a year (Texas, Maryland, Washington, D.C., New York, and California) at the times I lived there. However, my memory and experience go back only to the 1960s, and most of the instances I've found in print of "land office job" in an idiomatic sense are from the period 1944–1955. This is in contrast to "land-office business," which remains current and widespread, according to the sources noted at the beginning of this answer.

In all likelihood, "land office job" as an idiom was an offshoot—and perhaps merely a variant—of "land-office business." In most of the instances cited above, its meaning amounts to "brisk business" or "steady and perhaps demanding work." But if the usage ever was widespread, it didn't remained so for long; and at this point, it may be very local or restricted to individual families.