That is what you might call a tall order in the realm of ethics. In fact, the more you look at it the more the whole Sermon on the Mount smacks of (hopeless) idealism. Can anyone really do all this stuff? Is it even reasonable to ask?
The history of the interpretation of the Sermon is intriguing. There is a long tradition of avoiding its demands, toning them down to make them possible, or perhaps less universally binding than they appear to be at first glance. Especially in the established churches - from Constantine onwards - it has been usual to argue that the Sermon provides ethics for Christians in their private lives, but not in the public sphere, for example. Or it has been argued, in Lutheran fashion, that the Sermon represents Law (not Gospel), and is therefore only really designed to show us how far short we fall. It has tended to be radical movements - not all of them at all orthodox - which have taken the demands of the Sermon at face value. Sometimes this has led to thorough-going legalism, of which Tolstoy is a prime example, but not always. Sometimes it has led to radical Christian living.
It is worth observing two things about the structure of the Sermon. Firstly, it has at its centre the Lord's Prayer. Everything else seems to have been deliberately arranged around this prayer. I think Matthew intends us to see the sort of life Jesus describes in the Sermon as achievable, but only as the answer to the prayer: "your will be done on earth". The life of prayer comes before the life of radical obedience, and the latter is impossible without the former. Challenging. Moreover, the prayer assumes a relationship - God is "our Father" - into which we can only enter through Christ. Union with him, and relationship with the Father through him, is the sine qua non of the life of obedience.
Secondly, there are two passages in the Sermon, at roughly equal distance from the centre, which confirm this approach. In 5:13-16, Jesus describes the disciples as the salt of the earth, a city on a hill, a lighted lamp. Because they are all these things, they are to let their light shine before others, so that they may see their good works and glorify God. But it is clear that the good works emanate from a previous change in their existence, just as the light comes from the lamp having been lit by someone. Similarly, but from the opposite perspective, in 7:15-20 false prophets are to be recognised by their works - "a healthy tree cannot bear bad fruit, nor can a diseased tree bear good fruit". But the fruit does not make the tree healthy or diseased. That comes first.
So the Sermon demands radical obedience on the basis of a radical change that has happened to Christians and a radical prayer which invites God's action in their lives. If it looks impossible to me, am I perhaps thinking only in my own strength? Have I ceased to pray?