I'm replying to this after several weeks, so I won't be at all surprised if no-one reads it!

It does sound like a generalisation to me.  You don't have to think very long about the New Testament to realise that there are plenty of counter-examples - what about the parable of the talents, to start with?  Or the warnings to the Corinthians about their work being burned up?  Or James's words to inconsiderate rich people? 

And in the Old Testament Israel received God's blessings quite often in spite of her actions - protection from enemies, restoration again and again until the darkness of the exile, and even after that the restoration of a remnant to rebuild Jerusalem.

I would prefer to express your house group's leader's thought in a different way, perhaps something like this - throughout the bible we see a God of love, who gives good things to his people even when they fail him.  Actions, however, have consequences, which may include missing out on blessings God has in store for us, and although God can intervene he sometimes allows those consequences to run their course.  The big difference in the New Testament is that, because of what Jesus has done, we now know that there is no condemnation.  We may live with the consequences of sin, but we are saved and we will eventually be saved from its final penalty.  Not as pithy or as memorable as your leader's comment, I'm afraid.