The phrase the morning after the, or a, night before denotes the morning after an evening of drinking, when one has a hangover. In extended use, this phrase denotes the morning after any night of excessive revelry.

The earliest occurrences of the phrase the morning after the, or a, night before that I have found are as follows, in chronological order:

1-: From the paragraph concluding the account of the review of the Volunteers of the Mid-Western Counties, which took place in Gloucester on Tuesday 18^th September 1860—account published in the Cheltenham Examiner (Cheltenham, Gloucestershire, England) of Wednesday 19^th September 1860 (the phrase is in quotation marks, which indicates that it was already in current usage):

To-day Gloucester will doubtless relapse into its usual dulness [sic], and its appearance this morning will afford another exemplification of the familiar spectacle—“the morning after the night before.”

2-: From one of the unconnected paragraphs making up the column Fact and Fancy, published in the St. Albans Daily Messenger (St. Albans, Vermont, USA) of Friday 18^th July 1884:

The first governor of Alaska will be Kinkhead *. There is no official statement how it got so, but we presume the accident happened in the morning after “a night before,” when he tried to put on a 6⅞ hat on an 8½ head.—[Lowell Citizen.

* John Henry Kinkead (1826-1904) was the first Governor of the District of Alaska from July 1884 to May 1885.

3-: From The Boston Herald (Boston, Massachusetts, USA) of Sunday 23^rd February 1896:

PROBLEMS IN MODERN ARITHMETIC.
[From Judge.]

A woman purchases at a bargain counter 6 towels at 49 cents each, tearing her dress and losing her umbrella and temper in the crush. How much does she save by her venture, the regular price of the towels being 50 cents each?
In what proportion is the shrinkage of a man’s pocketbook to the swelling of his head the morning after the night before?
Cholly, whose salary is $8 a week, takes his girl to the theatre four times a month. How early in the spring must he pawn his winter overcoat in order to pay the instalments due on it?

4-: From the column The Stage and Platform, by ‘Loge’, published in Toronto Saturday Night (Toronto, Ontario, Canada) of Saturday 24^th October 1896:

A stage “drunk” is to me a fearful and wonderful mystery, and I should like very much to find out how it is done. The initiatory stages are simple and—may I say it?—familiar. Glass after glass is swallowed and the effect upon the victim becomes more apparent in exact mathematic proportion to the quantity consumed; that is to say, he is exactly twice as drunk when he has taken two glasses as he is after the first; and, after the fourth drink, precisely twice as intoxicated as he was after the second. This, I am told, is quite proper, and you watch the process with languid interest, moralizing fittingly meanwhile. But when the climax has been almost reached and the victim is just on the verge of hopeless intoxication, some emergency arises and, presto! he is instantly sober again. That secret is worth money to those who have reason to dread the next morning after “the night before,” and whose experience so far has been that the getting rid of a genuine “jag” is a painful, tedious and nauseating experience.

5-: From Differential Diagnosis of Headaches, read before the Houston District Medical Association in June 1898, by Joseph Mullen, M.D., published in The Memphis Lancet (Memphis, Tennessee, USA) of November 1898:

Toxemic headaches are due to the retention in the economy of a substance normal or abnormal that becomes toxic by its accumulation in sufficient quantities without any organic changes, or to the introduction from without of some toxic agent. Of the first class perhaps the most important and common is lithemia and uricemia, due to the accumulation of uric acid. […]
[…]
The second variety of toxemic headaches is well illustrated by the familiar example of a debauch, the headache of the next morning after the night before. The frontal headache of the excessive use of tobacco affords an excellent picture of this class. Both conditions rarely require anything more than the withdrawal of the drug and the administration of a nitro-muriatic acid and nux vomica.

6-: From the Grand Forks Daily Herald (Grand Forks, North Dakota, USA) of Tuesday 15^th November 1898:

THE NEW YORK ELECTION.
A Breezy Letter Giving Some Inside Points on the Late Campaign.

New York, Nov. 14.—(Special Correspondence.)—New York city looks today like a tired army after a long and exciting march. […]
[…]
It is well known that the administration was unable to pass any currency legislation, but it did pass the Dingley bill. New York was angry, but quiet. Then came the hundred days’ war and in the midst of her enthusiasm her anger was forgotten. Peace came, Montauk was far from a “Bromo-Seltzer the morning after the night before.”

7-: From the following cartoon, published in the Wilkes-Barres Times (Wilkes-Barre, Pennsylvania, USA) of Wednesday 22^nd February 1899—with allusion to some news item now forgotten:

THE MORNING AFTER THE NIGHT BEFORE.

O! Such a Headache!