[RummyChick]

and for the French side of it:

http://www.statue-de-la-liberte.com/en/Funding-of-the-statue-of-Liberty.php
When the idea of the construction of the statue was issued in 1865 there was only a vague project, interesting but that was part of a future not so concrete as that. When Bartholdi could look a little more seriously on that construction, he fell ill: The authoritarian government of Napoleon III, then head of government, prevented him from implementing a project statue of criticizing his regime, which was the hidden purpose the statue. The power of monarchical support in France was scuppered any attempt to public funding. Then, in 1870, the Franco-Prussian war broke out, leaving the land fallow. Bartholdi chooses exile in the United States, as much to escape her occupied country to discover that this young nation and to build relationships that allow him to make his statue. When he returned after the historic episode of the town is completed, the MacMahon government was still strong monarchical power. It took until 1875 for the Republican ideas are strong enough in the opinion that the government tends toward more openness, and he dismisses 1876 MacMahon. So it is not until the mid 1870s that the project of the Statue of Liberty was able to do.

[RummyChick]

And another part of the myth..it was REALLY about the French
http://www.travel-about.com/travel/10-fun-facts-about-the-statue-of-liberty-on-its-130th-birthday/

‘. At the time it was erected, Laboulaye simply hoped that the statue would spark a moment towards democracy among the French people—who, at the time, were subject to the repressive monarchy of Louis-Napoléon Bonaparte (Napoleon III).