I would think within the next month or so. He is just starting to heat up, but he has been striking out in about 1/3 of his at bats in the minors. He has had a huge past week and the Rays could use some change to generate runs. They are in 4th in the division, and if they promoted Myers, that would allow Zobrist to play second for the struggling Ryan Roberts or short for the struggling Yunel Escobar.
All speculation and sadly, no insider info...but we'll call it "educated speculation" that Myers gets a promo within the next 45 days. Considering his K history in the minors, he is not guaranteed to stay though.