There is no question that most Christians are not as generous as they should be with very few donating the minimum 10% of their income that the Bible teaches.In fact this issue more than almost any other except for the sin of second marriages makes some Christians enraged most probably because the capitalist dogma their churches teach them are is in opposition to Jesus' teachings to help the poor sacrificially.
Acts 4:32-35
The Believers Share Their Possessions
32 All the believers were united in heart and mind. And they felt that what they owned was not their own, so they shared everything they had. 33 The apostles testified powerfully to the resurrection of the Lord Jesus, and God’s great blessing was upon them all. 34 There were no needy people among them, because those who owned land or houses would sell them 35 and bring the money to the apostles to give to those in need.
Most of us do help people in need. You're right though, the majority of us are more concerned with our own salvation than that of others. However, some have the desire to help people, but they have nowhere where they can help.