“There is one day that is ours. Thanksgiving Day is the one day that is purely American” is a paraphrase of O. Henry (the pen name of William Sydney Porter, 1862-1910). The words come from the first two paragraphs of his short story, “Two Thanksgiving Day Gentlemen,” that was first published in the New York (NY) World in November 1905.
   
The O. Henry paraphrase has been included in many Thanksgiving quotation collections and printed in many images.
 
   
Wikipedia: O. Henry
William Sydney Porter (September 11, 1862 – June 5, 1910), known by his pen name O. Henry, was an American short story writer. O. Henry’s short stories are known for their surprise endings.
 
26 November 1905, Cincinnati (OH) Enquirer, “Two Thanksgiving Day Gentlemen” by O. Henry, sec. 3, pg. 3, col. 2;
THERE is one day that is ours. There is one day when all we Americans who are not self-made go back to the old home to eat saleratus biscuits and marvel how much nearer to the porch the old pump looks than it used to. Bless the day. President Roosevelt gives it to us. We hear some talk of the Puritans, but don’t just remember who they were. Bet we can lick ‘em, anyhow, if they try to land again. Plymouth Rocks? Well, that sounds more familiar. Lots of us have had to come down to hens since the Turkey Trust got its work in. But somebody in Washington is leaking out advance information to ‘em about these Thanksgiving proclamations.
 
The big city east of the cranberry bogs has made Thanksgiving Day an institution. The last Thursday in November is the only day in the year on which it recognizes the part of America lying across the ferries. It is the one day that is purely American. Yes, a day of celebration, exclusively American.
 
Google Books
The Trimmed Lamp:
And Other Stories of the Four Million
By O. Henry
New York, NY: Doubleday, Page & Company
1909
Pg. 50:
TWO THANKSGIVING DAY GENTLEMEN
THERE is one day that is ours.
 
Twitter
fred_dumas
‏@fred_dumas
There is one day that is ours. Thanksgiving Day is the one day that is purely American.
O. Henry
8:09 AM - 26 Nov 2008
 
Google Books
Toasts:
Over 1,500 of the Best Toasts, Sentiments, Blessings, and Graces
By Paul Dickson
New York, NY: Bloomsbury USA
2009
Pg. 214:
There is one day that is ours. There is one day when all we Americans who are not self-made go back to the old home to eat saleratus biscuits and marvel how much nearer to the porch the old pump looks than it used to.  Thanksgiving Day is the one day that is purely American.
—O. HENRY
 
YouTube
Two Thanksgiving Day Gentlemen by O.Henry (Pt.1)
13jalopy
Uploaded on Apr 26, 2010
From ITV’s “The Short Story”.
 
YouTube
Two Thanksgiving Day Gentlemen by O.Henry (Pt.2)
13jalopy
Uploaded on Apr 26, 2010
From ITV’s “The Short Story”.
 
Twitter
Nancy Ketner
‏@KetnerNancy
There is one day that is ours. Thanksgiving is the one day that is purely American. —O. Henry
#happythanksgiving
7:18 AM - 21 Nov 2016