Singer wrote "I always thought, 'Why that much — why not more?' "
Rabbinic commentaries on Deuteronomy 15 deal with the same tension
Devarim 15:7-8:

When there is among you a poor person, among your kin, in one of your cities, in your land which the Lord your God gives you, do not harden your heart, do not close your fist from your poor kin. Rather, you shall surely open your hand to him, and make him a loan, sufficient for his need, whatever he lacks.

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Does the Torah identify spheres of responsibility? What are reasons we harden our hearts to the poor?
What is the difference between leaving some of the harvest behind and making a loan?
How do you think we should determine how much another person lacks?
Midrash Tannaim

"Sufficient for his need" you are commanded to keep him/her alive, but you are not commanded to enrich him. "Whatever he lacks" everything is according to his sense of dignity, even a horse to ride upon and a servant to run before him.

They said about Hillel that he bought for a needy child from a wealthy family a horse to ride upon and a servant to run before him. Once he could not find a servant to run before him, and [Hillel] ran before him for three miles. A story of the people from the Upper Galilee who provided for a needy child from a wealthy family a pound of meat every day.

"Sufficient for his need" one who comes across a needy person is obligated to fill his lack, as it says "sufficient for his need." If one's hand does not reach far enough [to meet his needs], one gives as far as one's hand does reach. And how much is that? Up to one fifth of one's property is the best way to fulfill the obligation; one tenth of one's property is average; less than that is stingy.

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Is the story of Hillel to about how we should behave or about how Hillel behaves?
Tosefta Peah 4:8

We do not provide an itinerant poor person with less than a loaf of bread (about 1.5 pounds). If [the poor person] stays over night, [we additionally provide ] funds for lodging, oil, and a legume. If [s/he] stays over shabbat, [we provide] food for three meals, oil, a legume, fish, and a vegetable. When does this apply? When we don't know him/her, but when we know him/her, we also provide clothing. If the poor person goes from door to door, we are not obligated to provide everything.

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What would you consider “sufficient for his needs”? Consider the plight of the homeless and hungry.
How close is the Tosefta’s level of support to the support we give as a community/society?
Leviticus 19:9-11 9

When you reap the harvest of your land, you shall not reap all the way to the corner of your field, or gather the gleanings of your harvest. 10 You shall not pick your vineyard bare, or gather the fallen fruit of your vineyard; you shall leave them for the poor and the stranger; I the Lord am your God. 11 You shall not steal; you shall not deal deceitfully or falsely with one another.

Is there a difference between giving and setting things aside to be taken, and if so, too whom? Why might the Torah place the prohibition to steal right after the prescription to leave some of the harvest for the poor?
Or haHayyim

"When you (pl.) reap the harvest" begins in the plural and concludes in the singular "you (sing.) shall not reap all the way" is intended to contradict the opinion of those who mistakenly say that since there is not enough for all of the poor, he does not have to give, as if that one were saying "Why should I give this [little corner] when there are a hundred [poor people] in front of me?" For this reason, God commanded in the singular to say that even one individual has the obligation to give peah [i.e., even if others are not doing their part].

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Torat Moshe (Alsheikh):

You shouldn't think that you are giving to the poor person from your own property, or that I have despised him/her by not giving bread to the poor as I have given to you. For s/he is also my child, just as you are, but his/her portion is in your produce.

It is for your merit that I have intended to give his/her portion from your hand. And this is the reason why the beginning of the verse "When you reap" is plural, but the end "you shall not reap all the way" is singular. At the beginning it uses the plural "the harvest of your (pl.) land" ["your" meaning belonging to] the owner, the poor, and the stranger, for in truth, their portion is there [in the field].

Furthermore, the rich frequently hire the poor and strangers as harvesters, [referring to both] the owner and harvesters when it says "When you reap the harvest of your land" and afterwards, the command "you (sing.) shall not reap all the way" is commanded just to the owner.

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Which do you think is a greater "stumbling block" which prevents people from doing tzedakah, the enormity of the need or the feeling that other people are not giving so why should you?   How does a sense of inadequacy relate to a sense of isolation?    Do the problems described discourage you personally?
Leviticus 25:35-38

35 Now when your brother sinks down (in poverty) and his hand falters beside you, then shall you strengthen him as a sojourner and resident-settler, and he is to live beside you. 36 Do not take from him biting-interest or profit, but hold your God in awe, so that your brother may live beside you! 37 Your silver you are not to give him at interest, for profit you are not to give (him) your food; 38 I YHWH am your God who brought you out of the land of Egypt to give you the land of Canaan to be for you a God!

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Ramban

And this is the reason for "let your kin live with you" (Leviticus 25:36), that it is a positive command to keep him alive, and from this verse have we been commanded concerning the preservation of life as a positive commandment. And from here they said (in the Sifra): "Let your kin live with you."

Ben Potiri interpreted this as two people who were traveling on the road, and one had a canteen of water. If he drank, he would [survive to] get to civilization, but if both drank, both would die. Ben Potiri interpreted, "It is better that they both should drink and die, and the one should not see the death of his fellow."

[Ben Potiri maintained this] until Rabbi Akiva came and taught "'Let your kin live with you,' your life comes before your fellow's life." [Ben Potiri then] changed and said, "Let your kin live with you" by giving support and careful attention.

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Do you agree with Ramban? Does his answer surprise you?
Arukh haShulhan Yoreh Deah 251:4

And concerning that which they wrote about "his own sustenance takes precedence," if we take it simplistically, then most householders would be entirely exempt from tzedakah except for the third shekel.

For most of Israel has expenses which exceed their incomes, and therefore, except for the really rich, they would all be exempt from giving tzedakah. And in the places without rich people, the poor would be buried from hunger. How could one say this?! And surely the accepted practice is not like this.

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Are our needs or “sustenance” different from others? How do we understand the words “his own sustenance”?