The phrase to go to hell in a handbasket means to deteriorate rapidly; the word handbasket was probably merely chosen because it alliterates with hell, not for any rational reason.
This sense is absent from the Oxford English Dictionary (3rd edition, 2008), which also erroneously states that hell in a handbasket is of American-English origin, because the earliest instances that it has found are from books by American authors; the earliest quote in this dictionary is from The Great North-Western Conspiracy in All Its Startling Details (Chicago, 1865), by Isaiah Winslow Ayer (1826-1909):
At a meeting in the autumn, Judge Morris […] spoke, as was his custom, of the tyranny of the Pressdent [sic]; he said the rights of the people had been trampled upon, and the constitution had been violated by him. He referred to the suspension of the habeas corpus, and said many of our best men were at that moment “rotting in Lincoln’s bastiles [sic];” that it was our duty to wage a war against them, and open their doors; that when the Democrats got into power they would impeach and probably hang him, and all who were thus incarcerated should be set at liberty; that thousands of our best men were prisoners in Camp Douglas, and if once at liberty would “send abolitionists to hell in a hand basket.”
In his book, Ayer refers to Buckner Stith Morris (1800-79), mayor (1838-39) of Chicago, who was arrested in 1864 for aiding in a Confederate attempt to free prisoners of war from Camp Douglas in Chicago, and was acquitted in 1865. Buckner Stith Morris probably did use the phrase since, on Tuesday 14th February 1865, the Cincinnati Daily Enquirer (Cincinnati, Ohio) reported that during the trial of the alleged ‘Chicago conspirators’, a witness, William Hull, had declared:
Judge Morris […] said we had friends in Camp Douglas who were Puritans, or better than the Lincoln hirelings. He also spoke of giving these abolitionists hell under the shirt-tail, and about sending them to hell in a hand-basket.
However, the earliest instance of hell in a handbasket that I have found is from a letter by Feargus O’Connor (1794-1855), Irish Chartist leader, published in The Northern Star, and Leeds General Advertiser (Leeds, Yorkshire) of Saturday 23rd January 1841:
I am one of those who believe that the virtues of man, if cherished, and fairly displayed, very much preponderate over his vices. Sanctified hypocrites will tell you not, and that, do what you will, you are all to go to hell in a hand-basket, thereby, in fact, making you mere passive creatures in this world—passive to their will.
Another early occurrence of the phrase, also in the sense to go to hell, is from The Bolivar Bulletin (Bolivar, Tennessee) of Saturday 8th January 1870:
Dead Matter.—E. M. Stanton*, the Nero of the 19th century, died on the 24th of last month. “Gone to hell in a hand-basket.”
(* Edwin McMasters Stanton (1814-69), lawyer and politician who served as Secretary of War under the Lincoln Administration during most of the American Civil War)
On Thursday 25th January 1877, the editor of The Osage County Chronicle (Burlingame, Kansas) replied to various insults written about him by the editor of the Lyndon Times; one of those insults and the response were:
He’ll go to hell in a hand-basket.—[Lyndon Times.
While the editor of the Times will be “chucked in” with a fork.
The earliest use that I have found of to go to hell in a handbasket in the sense to deteriorate rapidly is from a speech about the USA’s moral situation that a certain Col. A. W. Slayback made at Bunker Hill, Ill., on Thursday 4th July 1878, as published in The Tribune (Minneapolis, Minnesota) of Saturday 13th July:
“Fraud in the pulpit, in the legislature, trickery and perjury, are heralded abroad until people believe the country is going to hell in a handbasket.”
Like that of hell in a handbasket, the earliest instance of heaven in a handbasket that I have found appears in an Irish context; on Wednesday 12th February 1834, The Wexford Conservative (Wexford, Ireland) gave a humorous account of a meeting that had taken place on Sunday 2nd at Crossabeg, a village in County Wexford—here, heaven in a handbasket has apparently a positive meaning:
If Mr. H. soared up to the Moon in his first flight of fancy, he mounted still higher in eulogising Mr. Morgan, whom, like another saint Paul, he carried, as it were, into the third heaven of adulation, as a good landlord—pictured him as a bright angel looking with benign glances of goodness on his tenantry and with a spirit of heaven born benevolence ministering to their necessities. […]
Such was Mr. H’s. pathos in describing the virtues of Mrs. M. that the sleeves and the tails of coats of the men, the corners of shawls, aprons, and other detached portions of the dresses of women were in great requisition—so much so, that until the sighing and sobbing had ceased, and all things partly adjusted, the speaker could not proceed; but as he went on it was only a repetition the same scene—but when he had landed the good lady in heaven in a handbasket, the eloquent Gentleman strewing her course thereto with vast numbers of her terrestrial golden actions in order to secure her celestial blessedness.
On the contrary, the second-earliest instance that I have found has apparently a negative signification; to go to heaven in a handbasket seems to mean to go to hell in the following from The Lincoln, Rutland, and Stamford Mercury (Stamford, Lincolnshire) of Friday 7th December 1849, which reported that during a trial at Lincoln County Court, a witness, William Hunt, had declared:
The lad Mundy was so wretched that sometimes he said he would poison himself.—Cross-examined: Had heard him say he would poison himself and go to Heaven in a hand-basket.
This would therefore be similar to the phrase to go to heaven in a wheelbarrow, meaning to go to hell, used by Thomas Adams (1583-1652), Church of England clergyman, in The Happines of the Church. Or, A Description of those Spirituall Prerogatiues wherewith Christ hath endowed her (London, 1619):
This oppressor must needes goe to heauen, what shall hinder him? But it will bee, as the by-word is, in a Wheelebarow: the fiends, and not the Angells will take hold on him.
However, to go to heaven in a handbasket has a clearly positive meaning in the following from The Fife Free Press, & Kirkcaldy Guardian (Kirkcaldy, Scotland) of Saturday 18th November 1871, which reported that, during a meeting of the Council of the royal burgh of Smelldungus,
Councillor Willow then proposed Councillor Webster as a fit and proper person for second bailie. He was a man gifted with every conceivable qualification for a seat in the Council, and in short, to use a common phrase, he might go to heaven in a hand-basket.