I was able to figure it out. I was not committing the .secrets file along with the R scripts. This is what I have in my script allow Heroku to upload into sheets.
gs4_auth(cache = ".secrets")
gs4_auth(cache = ".secrets", email = TRUE)
Here is what I ran to commit.
git add init.R file-name.R -f .secrets
git commit -am "commit reason"
git push heroku master
Maybe this is because I am new to R, but it was not clear in the gargle documentation that the .secrets file needed to be uploaded. I came across this information in this issue. Hopefully this can help someone else.