Yes, but

Today we here some of the most hash sounding words of Jesus in the gospel:
For it is not right to take the food of the children and throw it to the dogs.
This response from Jesus to the Greek mother of a sick child seems on the surface to be heartless. What we need to understand is a basic principle in how Judaism and in fact Jesus dealt with those who would be followers.
We can erroneously get the notion that Jesus simply throws the doors open and says, "Ya'll come." In fact, Jesus following Jewish tradition challenges those who would follow him, from what he says to the woman today, to when he tells the rich young man he must sell everything he has.

His words to the woman in the gospel were a test to find out if her faith was real or just a passing fancy.

Jesus loves us as we are, but at the same time constantly demands that we change. Grace is a free gift from God, but it requires a response.