I have heard it, and so have you. Maybe you've thought it or said it: "Didn't Jesus say that the poor will always be with us? So why try so hard to fight against poverty? Isn't it just a loosing battle?" I've been chewing on this for a couple of days, and just found an excellent article by Bryant Myers (author of "Walking with the Poor" a highly recommended book) on this very topic. I encourage you to read it, but I'll summarize it here and offer a couple of comments.
First, yes Jesus said something along these lines in Mark 14:7 (as well as John 12:8 and Matthew 26:11). In context, the disciples set-up a false dichotomy: they were upset at an extravagant offering of perfume which was related to Jesus' imminent death and burial. They felt that the money would have been better used to help feed the poor. From Jesus' reaction, it looks like the disciples were more interested in shaming the women than they were in really helping the poor.
But Jesus took their sinful attitudes and turned it into a teaching moment. He said that the woman's act of extravagant worship was a good thing because it was offered with pure motives in a genuine attitude of worship. So Jesus was setting priorities straight: God first, everything else second. Even our dedication to social justice and healing the hurts of the poor can become an idol, if we forget about God in the process. It is said that somebody asked Mother Theresa why she was called to serve the poor. She replied that she was not following the poor. She was called to follow Jesus, and she was simply following Him to the poor.
Another important element of these words of Jesus is that they are quoted from Deuteronomy 15:11. If you read that chapter, you will see that the whole point is that we need to be generous and open-handed toward the poor, because poverty is not something in God's original design. There is no indication in this passage that God is somehow reducing the pressure on His people to care for the poor. Quite the opposite!
So will the poor always be with us like Jesus said? Unfortunately, because of sin in the world, I think the answer to this is "yes". But there is coming a day when God's Kingdom will be fully here, and on that day I can confidently say that there will be no more poverty. Until then, we are called to follow God, and follow His leading in caring for the poor and working with Him in redeeming and restoring all of creation to God's ultimate, perfect design.