The FLOTUS is the commonly accepted term for the wife of an American president. It follows the model of POTUS (President of the United States) and SCOTUS (Supreme Court of the United States).
If the spouse of the American president is male, there is no settled title. First Gentleman is presumed to be the convention but this has not yet been tested.
Etymology/origin
These acronyms originated in the late 19th century as telegraphic abbreviations. The terms were adopted as jargon by those working in or around the White House and later passed into more general use.
Although the phrase First Lady of the United States is also attested from the 19th century, FLOTUS is more recent. The first OED citation is from the early 1980s, referring to Nancy Reagan:
To their Secret Service shadows they may be ‘POTUS’ and ‘FLOTUS’, but to each other out on their 688-acre California ranch he’s still her ‘Ronnie’ and she’s still his ‘Nancy’. 1983 Washington Post 20 Sept. c1/1 source
Usage
POTUS is used widely on the online, particularly amongst political bloggers. In a very partisan climate it serves the very useful purpose of emphasising the office rather than its holder e.g. POTUS on Eurozone compromise