Okay, this refers to Exodus 35 : 2:
"Six days shall work be done, but on the seventh day there shall be to you an holy day, a sabbath of rest to the LORD: whosoever doeth work therein shall be put to death."
This day would be Saturday and not Sunday. And as has been pointed out, only Jewish people treat Saturday as a holy day. For Christians, it's Sunday. In fact, I would counter that the New Testament invalidates this law with a few verses.
Matthew 12 : 11 :
"And he said unto them, What man shall there be among you, that shall have one sheep, and if it fall into a pit on the sabbath day, will he not lay hold on it, and lift it out?"
Colossians 2 : 16 :
"Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath [days]."
If you really want to argue about the morality of Exodus, ask a Jewish person. I'm an Agnostic from a Christian family, but I do read the Bible on a regular basis. If you read the New Testament, you see that the Jewish people were angry with Jesus and wanted to kill him because he healed people on the sabbath day. Given that the person who founded the Christian faith ran afoul of the Jewish law and got himself killed over it, doesn't that seem like a fairly powerful argument that Christians shouldn't necessarily respect those old laws? The whole book is pretty much an indictment of Pharisees and their obsession with legalism, rules, and rituals over actual spirituality.
I think that when Christ says he's come to fulfill the law, he means the prophecy of the messiah coming to Earth. He doesn't abolish the law, he is the ultimate sacrifice, the lamb of God, for all sins past and future. He takes the consequences of the law that imperfect humans can't fulfill onto himself and pays the price.