The government should take care of the poor, that is part of why we pay taxes. That does not mean that Christians should not, as obviously the governments are not perfect and people still need to eat. While Jesus took care of his own and many times provided food for the hungry, that was not the reason for coming nor the theme of his preaching. The scriptures show that we should help all that we are able to that are in need.
(Mark 14:7) For YOU always have the poor with YOU, and whenever YOU want to YOU can always do them good, but me YOU do not have always.
(Romans 13:5–7) There is therefore compelling reason for YOU people to be in subjection, not only on account of that wrath but also on account of [YOUR] conscience. 6 For that is why YOU are also paying taxes; for they are God’s public servants constantly serving this very purpose. 7 Render to all their dues, to him who [calls for] the tax, the tax; to him who [calls for] the tribute, the tribute; to him who [calls for] fear, such fear; to him who [calls for] honor, such honor.
(Galatians 6:10) Really, then, as long as we have time favorable for it, let us work what is good toward all, but especially toward those related to [us] in the faith.
(James 2:16–17) yet a certain one of YOU says to them: “Go in peace, keep warm and well fed,” but YOU do not give them the necessities for [their] body, of what benefit is it? 17 Thus, too, faith, if it does not have works, is dead in itself.
(2 Corinthians 8:12–15) For if the readiness is there first, it is especially acceptable according to what a person has, not according to what a person does not have. 13 For I do not mean for it to be easy for others, but hard on YOU; 14 but that by means of an equalizing YOUR surplus just now might offset their deficiency, in order that their surplus might also come to offset YOUR deficiency, that an equalizing might take place. 15 Just as it is written: “The person with much did not have too much, and the person with little did not have too little.”