It should be able to handle .357.
One issue with the K-frame .357s is potential cracking of the forcing cone due to being thinner on the bottom. There's a flat spot there. Do a google image search on "model 19 forcing cone" for a pic.
This is not the case with the Taurus 66. I had one of roughly that vintage.
"As was the man of dust, so also are those who are of the dust, and as is the man of heaven, so also are those who are of heaven. Just as we have borne the image of the man of dust, we shall also bear the image of the man of heaven. "