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1580s, flibutor "pirate," probably ultimately from Dutch vrijbuiter "freebooter," a word which used of pirates in the West Indies in Spanish (filibustero) and French (flibustier) forms, either or both of which gave the word to American English (see freebooter).
Used 1850s and '60s of lawless adventurers from the U.S. who tried to overthrow Central American governments. The legislative sense is not in Bartlett (1859) and seems not to have been in use in U.S. legislative writing before 1865. Probably the extension in sense is because obstructionist legislators "pirated" debate or overthrew the usual order of authority. Not technically restricted to U.S. Senate, but that's where the strategy works best.
1853 in both the freebooting and the legislative senses, from filibuster (n.). Related: Filibustered; filibustering.