I've written on this topic before so will repost it here:

Best that I can find, there wasn't much call for this. A little, which I'll touch on, but it seems to have been quite muted. Even by the time that the statue had arrived in the US, it had shifted from the red-brown copper it had shown off in Paris to a pure brown as the patination had begun (Thanks to /u/ducatimechanic here, this is a guide to visualize the change). It was fully expected that patination would occur, and for that matter, important that it would. Although Bartholdi apparently had hoped it would end up in a bronzed color, the statue staying its natural copper would be awful for it, structurally, and in restoration work that has happened, it has been important not to disturb the patina, because it is a layer of protection against the elements, which helps prevent further corrosion. Removing it, or worse, maintaining a continual cleaning schedule to prevent it at all, would just mean the copper would just continue to deteriorate away! This was of great concern in the '80s when a massive restoration effort was underway, especially when a cleaner being used on the interior seeped out and started to dissolve the patina in places, which workers had to quickly work to stop.

Checking through what literature I can find, the real issue concerning restoration has always been focused around who pays for it. The Statue of Liberty proved to be a somewhat awkward gift that left the US Government in a quandary, unsure quite what to do with it, and as such it fell into an administrative quagmire of competing jurisdictions. The National Lighthouse Board, the US Army, and the American Committee (the group which had fund-raised for the pedestal and operated ferries to visit), for various reasons, all had some level of responsibility, but also all insisted that the other groups were the ones who should be maintaining it. A 1890 bill was defeated in Congress that would have made is a public park maintained by the Federal government, and it wasn't until another decade had passed that Congress agreed to a small one time expenditure of $62,800, which was enough to do some interior painting and install the elevator, but hardly enough to anything more substantial, or long-lasting.

Now, to be sure, there was a good deal of public concern about this, and a number of newspapers, starting within a few years of the statue's arrival, decried this, but it doesn't seem to be about the color. As already noted, the patina plays an important role in preservation, and the only articles I could find from the time which makes reference to any calls to strip the patina are focused on explaining why it would be a bad idea! There were some people saying it should happen, but one author, writing in 1910, makes it fairly clear it was a proposal that was ignored:

The patina is the rust on bronze, which, however, does not, like the rust on iron, corrode the metal. It is green in color, the exact shade depending on the amount of alloy used with the copper to form the bronze. It is formed by the statue gathering from the atmosphere carbon and sulpher, and in the formation of nitrate copper crystals on the surface.

"In the case of the Statue of Liberty on Bedloe's Island" said Mr. [Gutzon] Borglum, "the continuous washing of the wain and the spray keeps it clean. I should have gone to Washington, if necessary, if the proposal to take away its patina had been likely to be adopted a year or so ago. People said then that it was eating into the metal, and that in certain placed the bronze was rent away. All I can say is, if there are any thin places they are the result of flaws in the original casting."

So again, as this suggests, there was clearly some people calling for the patina to be stripped, but from the start, experts were making clear that it was not needed, and a bad idea. An earlier article, from 1903, is even further in praise of the green, noting that of burgeoning hue at that point:

Kindly nature has been spinning for her a fine cobwebby outer raiment or verdanlique, deeper in one place, lighter in another. Snows and stinging hail, fogs and rainstorms have been gently removing the repulsive newness of her bronze and streaking cheek and uplifted arm, draperies and crown with tender shades or green such as the cleverest bronze rounders try to produce with chemicals on their new 'castings, but never quite succeed in simulating.

The author further warns against any voices which might "shriek wildly for scrubbing brush and Putz-powder", not just for the writer's aesthetic tastes, but also again for the protective covering the patina offers. The editorial also calls for the appointment of a 'keeper of public monuments', specifically to ensure ignorance doesn't result in the destruction of monuments, not just 'Lady Liberty', a position which seems to have at least somewhat come about by 1910, as that seems to be the role Gutzon Borglum was assisting in by then. Additionally, as before, this suggests the existence of those who desired a de-greening, but again that despite their existence, it was a call which experts pushed back against.

One related thing I did find, which I would also make mention of, was a call not for a stripping down to the natural copper color, but instead to paint it! An article in 1906 makes mention of such a proposal, and again the author instead favors the "marvelous harmony of blended colors" from the "varying shades of light green, delicate white, and a subtle dash of yellow" which by that point have almost entirely overtaken the bronzed hues. The proposal had been written up in several papers, but at least as presented in this article, but was clearly not in an advanced stage of planning. Capt. George Burnell, in command on the island for the War Department, mentioned to the author the "bushels of letters", almost all of which were aghast at the proposal - which additionally helps to point to the acceptance of the green quite quickly - and additionally talks to copper experts who find the idea not only unnecessary, but quite ludicrous. Unfortunately I was unable to find the original announcement, but it is certainly clear enough that it all came to naught.

Anyways though, to continue with this more general over view of restoration, during the Wilson Administration, a Public-Private partnership with the World newspaper saw another $30,000 from the government, but again, it was a one time expenditure, and this time for installing flood-lights. Lights which, lacking maintenance funds, had mostly ceased working by 1930.

This funding morass continued through the 1930s, when it finally was moved to the jurisdiction of the National Park Service, as part of a larger push under the FDR administration, in step with the New Deal, to give 'Lady Liberty' her due as a symbol of the country. Unable to get the funds solely on its own, between 1937 and 1941 the NPS worked in conjunction with the PWA and WPA to give the statue its first real overhaul, a $1.5 million dollar makeover which involved clearing the entire island of buildings to start fresh, building a seawall, a new dock, walkways, and most importantly much needed maintenance of the internal iron structure - although not quite extensive enough - which was becoming quite rusted at points, thanks to the salty seawater surrounding it. Much was done, but of course the outbreak of war in late 1941 brought it to a halt. Work would resume again in 1946 to wrap up work unfinished in '41, but over the next decade or so, the real focus with funding was on the creation of an American Museum of Immigration, which would eventually open in 1972 after a long and fraught 'battle'.

By 1981, even the work done by the NPS decades earlier was showing its age, and spurred by an analysis by French architects, a renewed focus on a thorough overhaul of the statue, especially in light of the upcoming centennial, began to be planned, perhaps most famously with American Express donating a penny for every purchase made with their card to the endeavor, resulting in $1.7 million dollars. Closed to the public in 1984 for the work - and as noted above, careful not to disturb the green! - the work was completed in time for the "Liberty Weekend" centennial celebration in 1986, with President Reagan turning on the floodlights the night of July 3rd, and the statue officially reopened on the 5th.

Berenson, Edward. "The Statue of Liberty: A Transatlantic Story" New Haven: Yale University Press, 2012

"BRONZE MONUMENTS IN PERIL." New York Times, May 18, 1903.

"How Shall "Miss Liberty's" Toilet be made?" New York Times, Jul 29, 1906.

"SPRING CLEANING FOR CITY STATUES." New York Times, Mar 03, 1910.

ProQuest News and Newspapers Database, Various Searches