1570s, "bog, marsh," from obsolete quag "bog, marsh" + mire, n.. Early spellings include quamyre (1550s), quabmire (1590s), quadmire (c.1600). Extended sense of "difficult situation, inescapable bad position" is recorded by 1766; but this seems to have been not in common use in much of 19c. (absent in "Century Dictionary," 1902), but revived in a narrower sense in reference to military invasions in American English, 1965, with reference to Vietnam (popularized in the book title "The Making of a Quagmire" by David Halberstam).