I think one of the things that modern Western Christians don't realize is that the goal of taking care of the poor among them is to remove the need entirely in their midst. In other words, as you want to get rid of a need your child may have, so that it is provided for adequately, the church should want to also remove such a need from their brothers and sisters in Christ. The failure to understand that giving to the poor has the purpose of alleviating the Christian of his need has caused Western Christians to think that they do just fine in taking care of the poor, and have plenty left for unbelievers too.
Acts, however, presents us with a very different picture.
"They were devoting themselves to the apostles’ teaching and to fellowship, to the breaking of bread and to prayer. Reverential awe came over everyone, and many wonders and miraculous signs came about by the apostles. All who believed were together and held everything in common, and they began selling their property and possessions and distributing the proceeds to everyone, as anyone had need. Every day they continued to gather together by common consent in the temple courts, breaking bread from house to house, sharing their food with glad and humble hearts, praising God and having the good will of all the people. And the Lord was adding to their number every day those who were being saved." (Acts 2:42-47)
First, we see that giving wasn't so minimal that it didn't take much sacrifice to give it. They sold houses and properties that would have made them quite the sum of money to keep. They gave much because much was needed to meet the needs in their midst.
Second to this, they gathered together every day in order to fellowship and meet the needs of poor Christians. These needs had to be met on a daily basis, or Christian brothers in poverty would go without.
In other words, the greatness of the needs required daily provisions, so that the need was completely addressed. Take another example from Acts.
"The group of those who believed were of one heart and mind, and no one said that any of his possessions was his own, but everything was held in common. With great power the apostles were giving testimony to the resurrection of the Lord Jesus, and great grace was on them all. For there was no one needy among them, because those who were owners of land or houses were selling them and bringing the proceeds from the sales and placing them at the apostles’ feet. The proceeds were distributed to each, as anyone had need. So Joseph, a Levite who was a native of Cyprus, called by the apostles Barnabas (which is translated “son of encouragement”), sold a field that belonged to him and brought the money and placed it at the apostles’ feet." (4:32-37)
This exclusive financial focus on the church as the recipient of early Christian charity gave the church the ability to annihilate poverty among its members. Indeed, as v. 34 states, "there was no one among them who were needy" because of their giving to one another. The need was completely satisfied.
But such an accomplishment was only possible because physical resources were focused on the Christian community, and needs were met daily. For instance, there was a daily serving of food to the widows (Acts 6:2), showing that Christian giving was meant to take care of another believer's total need, not just an activity where someone throws a couple bucks their way or takes care of only part of the need, or does not take care of the need daily.
In other words, Acts tells us that the goal of Christian giving is not to just throw some ineffective charity at poor Christians, but to actually take care of the total need. The church is only capable of doing this when all giving is focused on the Christian community. There is daily shelter to provide and daily food and water to supply.
Part of the problem of Christian general giving is that Christians do not realize what taking care of the poor among them actually requires. Hence, they think they have plenty to go around, simply because they are not actually taking care of the needs among them.
It is easy to give someone a bottle of water or some left over food or some junk laying around, but how will that Christian be sheltered from harsh weather and be filled with food and have his thirst addressed on a daily basis? Some old junk may be useful in some way, but it won't pay his rent. Some scraps of food will feed him that day, but not his family for the next week or month.
Right now, the way that Christians view giving, does nothing but make charity a self-glorifying and feel-good act that contains very little sacrifice and care for the person who is receiving such charity.
General waste and a general concept of charity has also depleted most churches of the resources they need to accomplish the task to which God has called them. It is no wonder that judgment, expressed in confusion of what the Bible says in general, a giving over to sexual depravity, and economic difficulty, has come upon the church, which, according to the biblical model, is not taking care of its poor in the way that it is supposed to take care of them.
If nations are judged for not taking care of their poor, then certainly the church, as THE nation, will be, and likely is being, judged for it.
This burden is placed on the church as a whole, as Christians individually merely contribute whatever they can to meet the need, and collectively are able to alleviate poor Christians from that need. Our goal is not to merely throw some charity at it, but to actually remove the need itself, the giving of the many sacrifices becoming the larger pool that enables the church to do just that.
The general sentiments of the social gospel in the church, however, have gotten in the way of this goal. Churches are poor, even though their people are not. Money goes to religious shysters who buy extreme luxuries for themselves. It goes to supporting unbelievers in general around the world. It goes to private luxuries of individual Christians. And it goes to sermon props, carnivals, and to build giant monuments that supposedly teach us about the Bible through image. All contribute to our unfaithfulness in the area of taking care of our widows, orphans, blind, deaf, disabled, sick, out of work, etc. in the way that we should.
Perhaps, the real question may be, not whether the Western church should be taking care of poor believers and unbelievers alike, but whether the Western church has been taking care of the poor at all.