The American Dream is a modern ideological construction dating to the mid-twentieth century. Historian James Truslow Adams coined and used the phrase in his 1931 book The Epic of America. For Adams, the newly invented "dream" was an ethical one, according to Jeffrey Louis Decker in Made in America, that revolved around ideas of justice and opportunity, ideas such as: a future better world for all, economic and financial opportunity for all, social justice for all, and liberty for all.
To try to apply these ethical post-World War I, Depression sprung ideas to Revolutionary, Colonial and American Gothic short stories and their authors may be anachronistic (out of place with the time written about), though identifying sympathetic themes might allow association with the American Dream. One might accept the supposition that the ethical dream has always imbued the hearts of American colonists and early citizenry, though difficult to prove historically.
What themes are in these stories that may coincide with the Depression Era inspired pronouncement of the American Dream? In Irving's "Rip Van Winkle" (1819), a dominant theme is liberty (personal and social) in pre-Revolution and post-Revolution America. This is shown from several perspectives, including Rip's liberty run amok. The final lines of the story feature American liberty, where order and purposefulness reign and even Rip's wild liberty can be tamed and lent to--if not usefulness--entertaining purposes in a new social order that does offer a better future for seemingly all. If Irving had a "dream," liberty and a better world for future generations would seem to be it as Rip transitions from the status of ignorant subject to knowledgeable citizen.
In Hawthorne's "Young Goodman Brown" (1835), set in colonial America, a dominant theme is religious liberty, which is shown as having an effect on future generations, one which ironically lessens true liberty. Hawthorne's concern was the imprisoning effect and real origins--though metaphorically expressed--of Puritan rigidity and atrocities. If anything, it might be said that Hawthorne's story presents opposition to the American Dream as liberty is traded for the tyrany of devilish forces, which is what Brown shows in his transition from spiritual ignorance to devilish knowledge. It might be said that perhaps Hawthorne was placing the nineteenth century's blamable economic greed at the feet of the colonial Puritans whom the story shows as relentless.
In "Tell-Tale Heart" (1843), personal liberty seems again to be the overriding theme of this story, which has no specifically identified time setting.
And every night, about midnight, I turned the latch of his door and opened it --oh so gently!
There seems no way to apply a sympathetic thematic idea to that of the American Dream. If it be personal liberty, it is a twisted personal liberty. It certainly cannot be that of a better future. Nor can it be that of social justice, as there is no justice in the madman's actions as he moves from ignorance of his fiendish skill to knowledge of its accomplishment. Perhaps we might analyze this allegorically and say Poe meant the madman to be political oppressors of social justice and liberty who are brought to justice themselves. This would accord with the American Dream's ethical ideology of social justice for all, though in the story it is applied backwards against oppressors instead of forward for citizens.