No specs for a potential 3060 have been published yet that I have been able to find. A price target of $399 is being floated, though. Also, no word at all about Big Navi.
Edit: since my original response, some specs about a potential 3060 Ti have come to light, but no confirmation from Nvidia about it, yet. I'm guessing they are binning more 3070 chips with defects than they expected they would and are creating a slower card to dispose of them. A vanilla 3060 with lower specs is probably the planned release. 4864 CUDA cores, 152 Tensor cores, 38 RT cores, and 8gb of GDDR6 on a 256 bit bus delivering 448Gbps bandwith are the early numbers that are being floated. Power consumption is estimated at 180-200W. They are saying performance will be around that of a vanilla 2080, but the memory aside, it has more CUDA cores than a 2080 Ti, so maybe performance will be higher than a vanilla 2080, but less than a 2080 Ti on account of the memory. A price target of $300-$350 was also mentioned. From the above specs, it certainly sounds like a 3070 with a crippled GPU because most everything else matches up with that card.