I don't think Steinbeck portrays George as a hero. One of the main themes of the novel is friendship and loneliness. George and Lennie have a special friendship unlike any of the other chararacters. This friendship keeps them from being isolated and lonely like the other guys who go from place to place and never make more than casual friends. But George needs Lennie as much as Lennie needs George because he needs someone to take care of just as much as Lennie needs someone to take care of him. Yes, Lennie gets into trouble, and George must get him out of it, but does this make George a hero? This makes George a good friend who is like a parent to Lennie, but anyone who is a parent takes care of his child because he loves him and feels responsible for him. Parents get tired sometimes and wish they could have time away from their child, and this is how George feels when he complains about Lennie. At the end of the novel, George does for Lennie what any good parent would do for a child. He keeps Lennie from having to suffer, allowing Lennie to die happy thinking of their dream.
George is a hero because he is try to preserve his dream and that of Lennie. He is trying to carve out a place where a person like him can truly be free and have some sort of control over his life.
Steinbeck is lamenting the poor conditions and opportunities that life held for people like George and the ranch hands during the 1930s. He is trying to say that the world would be a better place if people like George had a chance to get ahead in life ande realize their dreams.
Steinbeck liked to take the underdog an make him into heroes of an odd type in his stories. George is not the average hero. He is not tall and strong. Instead Steinbeck purposefully made him the smaller of the two men, but he is the smarter of the two. Steinbeck did not give George great genius but made him an ordinary man trying to etch a living out of whatever work he could find.
George is the kind of man who would never find himself to be a hero. He takes Lennie with him places because he feels that it is what he should do. He does not over think it, he just does it. Taking care of Lennie also gives George a different purpose in life. It sets him asie from the other men and helps him not to feel that there are no dreams. He has a companion as he goes from place to place.
The hero part lies in the imbalance that Lennie places on their lives by always getting himself into trouble. George could have walked away from it or let Lennie receive his consequences but George cares about Lennie. George has a good heart and knows how dependent on him Lennie really is. George sticks by Lennie despite all of the problems.
Lennie's death is just one more way that George does the right thing for Lennie. George's role as a hero takes away something good from a tragic situation. In George one is able to see hope, love, ad concern for other human beings. He is the most extraordinary of an ordinary man.