It's not about the rules.  Too many times have I heard "God creates us, then sets the rules in opposition to 'human nature'" and it's just not true. 
God created the laws to prove that man can't do it alone.  "The requirements of God's holiness, righteousness, and glory were so great upon us that it was impossible for us to fulfill them.  However, God paid the price for us through Christ, repossessing us at a tremendous cost" (Romans 3:24, Footnote 3).  Whenever we wander from God, he pricks our conscience to bring us back to him. 
There is a Jesus-shaped hole in our souls...what do you think goes in there?  Too many times I've tried to fill it with something else (see my Lord of the Rings incident for more details) and it has just resulted in unfortunate results.  Jesus fits as part of our belief and as part of our spiritual life. 
Is there something naturally good in every person?  Yes...the conscience..
"For all have sinned and fall short of the glory of God" (Romans 3:23). 
It's not even about keeping the's just about following Jesus. 
The Jews are God's Chosen people, but they haven't accepted Jesus as their Savior.  This is the only Way.