Yes, he can send the bill back to congress. What does that do but delay the implementation of the good parts of a bill? The president can only ignore such passed laws that affect his executive decisions. He need not send a bill back for that.
Are you of the opinion that congress can tell a president what he can and cannot do? Do you really believe congress should be elevated above the president? Don't you believe in the three equal powers?
How many signing statements have you ever read? I suggest you read several, and see what most say.