The impossibly difficult instructions found in the sermon on the mount have often troubled me.
When I think about loving enemies, turning the other cheek, giving to the poor, storing up treasures in heaven, etc... I often feel like there's NO WAY I can be successful in the correctives Jesus presents.
With that said, I think Oswald Chambers speaks to the dilemma incredibly well in his devotional, "My Utmost for His Highest", and here is what he says:
"The Sermon on the Mount is not an ideal, it is a statement of what will happen in me when Jesus Christ has altered my disposition and put in a disposition like His own. Jesus Christ is the only One Who can fulfill the Sermon on the Mount."
I think this quote can be helpful when preaching through the Sermon on the Mount and/or even when preaching through being a 'New creation IN Christ'.