The thanksgiving one-liners are more often related to the history of thanksgiving. Also there are other things too like turkey, the Indians, pilgrims, general traditions etc which are targeted in these one-liners for some harmless fun. Some of the thanksgiving one-liners are given below:

• "Why did the turkey cross the road?
  It was the chicken's day off."
• What’s the best dance to do on Thanksgiving?
  The turkey trot"

•  “Why did the police arrest the turkey?
  They suspected it of fowl play”
• “Can a turkey jump higher than the Empire State Building?
  Yes - a building can't jump at all”
• “If the Pilgrims were alive today, what would they be most famous for?
  Their AGE”
• “What do you get when you cross a turkey with an octopus?
  Enough drumsticks for Thanksgiving”