There seems to be the idea that the private sector could never, ever match the level of redistribution through taxes and therefore people would starve in the streets if such programs discontinued.
That is very likely not true for several reasons.
Let us look at 10$, redistributed by the government. All in all as little as 30% reaches those who were intended to be helped with the program.
That is not all, however.
The 10$ taxed could have been 12, or 13 or even 15$ were there no progressive taxation, because progressive taxes work as a disincentive whereas charity works as an incentive.
Less technically, if people are heavily taxed they work less because they perceive it as a punishment. When they give to charity however, they feel all warm and fuzzy and are proud of themselves, so they might even work more to be able to give!
The other part we need to look at is the 30% that reaches those who are the recipients of those programs. One simply cannot use the money figures , what matters is utility. As an example, if the government buys an Eskimo a refrigerator for 300$, the Eskimo has not exactly gained 300$ in utility, in fact the refrigerator is a nuisance. Very often that money goes to programs the poor do not really want or need, so all of it is simply a make work program for the politically well connected middle class.
In conclusion, there is no reason to believe that private charities would waste as much money as government programs, so private contributions would be a significantly smaller percentage of a significantly larger pie.