'I will put my law within them, and I will write it on their hearts' (31:33), does not go beyond the expectations of the Mosaic Law itself (Deut. 30:14). According to the Shema (Deut. 6:6), God always intended that the law be internalized in the hearts of his people.
The New Testament Lord's Day, is part of a greater issue of the law and gospel theology as taught by Luther, Calvin, the Puritans, and the great Reformed confessions, versus the new covenant theology of today.
There Remains a Sabbath Rest for the People of God (iii)