Welcome to FT!
Where are you starting? As mentioned, Delta doesn't fly to Tahiti but Air France and Air Tahiti Nui do - both from LAX. A quick look at Expertflyer indicates that there aren't any seats on either airline on your dates +/-3 days. I imagine it's a popular time given the holiday.
You can keep checking on Delta.com for Air France awards. Air Tahiti Nui isn't available on Delta.com so you will need to call or use Expertflyer to find space and then call.