The colloquial American-English phrase tough titty, also tough tiddy, is used as a way of telling someone that they will have to accept a situation they do not like because they have no choice.—Synonyms: tough luck, tough shit.

The noun titty, also tiddy, denotes a teat, and, in this phrase, the image is of sucking a tough teat.

This image is clear in the text containing the earliest occurrence of tough titty that I have found; this text is from the Bristol Courier (Bristol, Tennessee) of Thursday 17^th May 1888, which deplored the re-election as Governor of Tennessee of the U.S. politician, author, magazine editor and public lecturer Robert Love Taylor (1850-1912):

For Governor,
HON. R. L. TAYLOR, of Washington.

Grease it, swallow it, and spit quick.
Yes, sir, the frost fell ere Robin nested again.
It’s tough titty, boys, but let’s suck it like little men.

The second-earliest occurrence of the phrase that I have found is—as tough tiddy—from The Lowell Daily Sun (Lowell, Massachusetts) of Tuesday 27^th March 1894:

BOWLING NEWS.

It was “tough tiddy” for the Lowells last night to be thrown down with three men over 500, and one of these got a three-string total to tie the previous record.

The phrase then occurs in the account of baseball games, published in The Philadelphia Inquirer (Philadelphia, Pennsylvania) of Tuesday 2^nd September 1902:

From The Sporting Editor of The Inquirer.
St. Louis, Sept. 1.—The truth must be told, no matter how painful. That is the disagreeable end of the work of The Inquirer was correspondent “on the spot.” If there was only some way in which he could let down the Quakers easily it would not be so bad. If he could only damn Sheridan for possessing an oblique vision in the matter of balls and strikes, or throw the harpoon into Johnson for failing to call out the St. Louis runners when they were in, or calling safe the Athletic runners when they were out, it would not be so bad. It would be a sort of balm. But, as a matter of fact, Sheridan was all right on balls and strikes, and Johnson was all to the good so far as the base decisions went. The fact is, that, taking them collectively, the Browns played the better ball at both performances to-day, and there you are. It is tough titty, of course, but such is the noble national game.