Google's John Mueller said on Twitter that Google doesn't have an organic traffic budget that will stop sending a site traffic once it reaches a certain number. He said "we try to show pages in search when our algorithms think they're relevant, not based on counters."
Here are the tweets:
No, there's no "organic traffic budget" - we try to show pages in search when our algorithms think they're relevant, not based on counters.
— 🍌 John 🍌 (@JohnMu) March 14, 2019
This is not the first time Google had to answer this question.
In 2016, Google had to confirm they don't throttle traffic to web sites and once again later that year.
So once Google sends your page 1,000 visitors in a single day, it doesn't mean Google can't send you twice as many.
Forum discussion at Twitter.