“Gobble ‘til you wobble” (or “Gobble till you wobble”) is a saying that has been printed on many images. The Thanksgiving expression has been cited in print since at least the late 1980s.
 
       
4 November 1989, The Sun (Baltimore, MD), “24 Hours,” pg. 1D, col. 6:
“Gobble ‘til you wobble” at St. Francis of Assisi annual turkey dinner at 6 p.m. at the St. Francis Church Hall, 3615 Harford Road.
 
24 November 1989, News Record (North Hills, PA), pg. 14, col. 1:
Valentine’s, 4869 McKnight Road. Friday Gobble ‘Til You Wobble Party.
 
3 November 1990, The Sun (Baltimore, MD), “24 Hours,” pg. 1D, col. 3:
Gobble till you wobble at the annual turkey dinner at St. Francis of Assisi Church.
 
21 November 1990, The Orange County Register (Santa Ana, CA)< "Indian dancers to visit Irvine" by Anne Valdespino, pg. I2:

Gobble till you wobble . . . More than 600 turkeys, 13,000 sourdough rolls, 12,050 pumpkin pies, 2,100 pounds of dressing and 2,100 pounds of mashed potatoes with giblet gravy will be on the menu at Knott’s Berry Farm’s annual turkey feast.
     
Google Groups: rec.arts.bodyart
tattooed librarians?
.(JavaScript must be enabled to view this email address)
11/23/93
(...)
Peace…and happy turkey day!  gobble till you wobble!
 
Google Groups: rec.travel.cruises
HOLIDAY WISHES
JO WALKER
11/27/97
(...)
Oh, go ahead, gobble ‘till you wobble!
   
Google Groups: alt.disney
“Eisner could pay that out of his own pocket…”
David M. Bugg
11/25/98
(...)
I hope you have a wonderful Thanksgiving holiday—- gobble til you wobble.
 
Google Books
The Business of Holidays
By Maud Lavin
New York, NY: The Monacelli Press
2004
Pg. 214:
Those who did not probably went to places like the Martinique Restaurant in Evergreen Park, Illinois, where the Thanksgiving Day motto is “Gobble till you Wobble.”
   
Twitter
Claire Díaz-Ortiz
‏@Claire
Back from dinner at the unfortunately titled “Gobble till you wobble out” cafe. Good times, babies screaming…how does sis use lather, clara?
7:53 PM - 14 Dec 2006
 
Twitter
Lisa A
‏@LAlconcel
To all my Twitter Friends… Happy Turkey Day! Gobble ‘til You Wobble!
11:06 AM - 21 Nov 2007
 
Twitter
ZumbaInTheBerkshires
‏@ZumbaBerkshires
Happy Thanksgiving Sarah and Aaron—Gobble till you wobble!
4:13 PM - 22 Nov 2007
 
Google Books
The Encyclopedia of Greeting Card Tools & Techniques
By Susan Pickering Rothamel
New York, NY: Lark Books
2008
Pg. 283:
THANKSGIVING
(...)
Gobble ‘till you wobble!
   
Google Books
Tinsel:
A Search for America’s Christmas Present
By Hank Stuever
Boston, MA: Houghton Mifflin Harcourt
2009
Pg. 36:
One co-owns a company called Two Funny Girls, selling holiday- and sports-themed Styrofoam party cups — “Gobble ‘til you wobble” reads one with a turkey on it;
 
Twitter
Peridot Impressions
‏@peridotimpress
Gobble Til You Wobble - Thanksgiving - 5"x7” Invitation by PeridotImpressions http://etsy.me/2fxuGpa  via @Etsy
5:44 PM - 22 Nov 2016