Who is Matthew's intended audience for the Sermon on the Mount?

Question

On another question, I've received several answers to the effect that the ethical teachings of the Sermon on the Mount aren't terribly relevant to Christians— that they were given to people under the old covenant in order to lead them to the new covenant. Certainly some of the ethical teachings of the Sermon seem an impossibly high bar to follow.

Does Matthew expect Jesus' disciples (post-narrative) to live up to the standards set in the Sermon? In other words, is the Sermon for Christians? Or is the purpose of the Sermon to raise the bar of the law so high that the only recourse left to the hearer is to plea to the judge for mercy? Or in other words, is the Sermon for those who do not believe?

Answer 1

The Sermon on the Mount begins with the beatitudes, the first of which sets the context for the whole sermon.

Blessed are the poor in spirit, For theirs is the kingdom of heaven.
-- Matthew 5:3

Who are the poor in spirit? Well, anyone who is spiritually needy, of course. Those who know they're lives are becalmed and need some "wind" in their sails to get them moving. Jesus identifies these needy ones as the mourners, and the meek, and the hungry and thirsty for righteousness.

Those who don't mourn are rich and have no need of comfort. But, if they don't exercise mercy then they will never know the mercy of God.

Those who have great power make themselves rich by taking the earth. But, if they're not making peace then they will forever stand outside the family of God.

Those who consider themselves righteous are already rich. But if they're not pure in heart they will never stand in the presence of God.

Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt, and where thieves break through and steal: But lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal: For where your treasure is, there will your heart be also. ...

Therefore take no thought, saying, What shall we eat? or, What shall we drink? or, Wherewithal shall we be clothed? (For after all these things do the Gentiles seek:) for your heavenly Father knoweth that ye have need of all these things. But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you.
-- Matthew 6:19-21,31-33 (KJV)

I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see.
-- Revelation 3:18 (KJV)

Conclusion

The Sermon on the Mount opens with an advertisement -- an advertisement for the treasures of heaven, and Jesus is the doorway into the treasure house. Jesus' audience, then, consists of anyone who is interested in buying what he has to sell.