According to the latest rumors from BenchLife, NVIDIA's GeForce GTX 1060 will arrive in time to compete with custom Radeon RX 480 cards.
If the rumor is correct, and the site does have a decent track record of leaks, the official (paper)launch date will be July 7th, with actual retail availability slated for a week later on July 14th.
The rumors are that GTX 1060 will feature GP106 GPU with around 1280 CUDA cores, 3GB and 6GB variants and 192-bit memory interface. According to the same website both of these variants will use different GPU models: GP106-300 (3GB) and GP103-400 (6GB).
The GeForce GTX 1060 was originally planned for August but word on the street is that NVIDIA moved the launch to July to better compete with AMD.