Government aid makes individuals and families dependent on the government, provides a disincentive both by rewarding unemployment and by increasing taxation and is building a massive national debt. Having stated all of that, it may be necessary. Private charities have none of the negative effects and all of the positive effects of government welfare, but can they provide for the needs of as many people as the government? The government is inefficient, but it is large enough to fill this role. This is the critical question: If all government aid, including Social Security, which is a terribly planned Ponzi scheme, were eliminated, could private charities fill the void- and if so how quickly?

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"I am a Tory Anarchist. I should like every one to go about doing just as he pleased- short of altering any of the things to which I have grown accustomed." (Max Beerbohm)

It could.
It's a cultural issue more than anything else. One of the things that terrifies me more than anything else in this country is the prevalence of young conservatives (and even some liberals) that feel that personal responsibility applies only to one's own welfare in a very limited sense. Quite often they talk in half-@$$ed economic terms trying to make it sound as if their self-indulgence is somehow altruistic. It's also problematic that most people feel that they are struggling whether they are or not and thus feel that they have nothing to give. To some extent a lowering of taxes may reduce this struggling but since in reality this struggle is primarily mental, I don't think it would do much to increase charity.
Another problem is that the way we are used to doing charity, whether government or private, is cheap but inefficient. We just hand out rather than applying toward training, education, childcare, recovery, or whatever the actual issues are. There is change, but it is slow.
In order to see more charity, charity must become more profitable. Since the people who use charity don't have money to speak of, this profit can't be financial and still be well-targeted unless it comes completely from third party sources- which requires a higher propensity in other firms and people to give. The idea that taxes get in the way of charity is assumptive that money taken out of taxes would go to charity anyway, but more efficiently. Somehow I doubt that.
To make private charity or any charity actually work well requires a shift back in attitudes. Our society is beginning to place too much social prestige on self-gain for the purpose of self-gain, pure selfish materialism, and rationalizations that tell us that what we do for ourselves is somehow automatically and universally helping others without any effort from anyone to direct it. Most civilizations throughout time have placed a greater emphasis on contribution and the ability to give. In the past this was what gave governments legitimacy and it continues in the form of welfare.
To take government out of the picture requires people to do government's job. People should take pride in what they give not in what they have. And as consumers and voters we should support those that offer something to society rather than those that hoard.
How can we expect people to want to work for what they want when it is what they want that really matters in the end? How can we expect that people will turn their lives around when we make every excuse for our every indulgence and offer the less fortunate nothing but half-@$$ed fortune cookie advice?
As I've been pointing to for a while, government exists because it has a niche. We can either do its job and get rid of that niche or we can accept its growth at the expense of our freedom. What we can't expect is that suddenly people are going to give up and die when they've run out of rational choices rather than choosing deviant paths or that people will suddenly become more rational without more available information or that people with too few resources to make rational choices will more often take irrational risks of that little bit they have for a tiny chance of slight growth. And we can't expect that people are going to reach their best potential when no one will offer a hand.
It's really up to us. We either do the things that need to be done and increase our freedom and efficiency in the process or we accept that government is easier and we might as well do it that way despite its limits. Actually it's a continuum, so don't worry too much on absolutes. I don't expect we'll reach either extreme in our lifetimes.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside

We have private charities now. They don't seem to be able to. Sadly, I feel humans as a whole are too greedy to willfully contribute enough to charity to help the less fortunate ones. That being said, a serious overhall needs to be done with the current system. I have seen plenty of people on welfare who are better of financially than others that won't be allowed to have it.

Furthermore, when speaking of national debt, I think there are many other areas that could use cutting before going to programs that actually help people.

This is only a tentative proposal, but what do all of you think of it? We could merge all government aid (excluding Social Security) into one agency and then turn that agency into a private, fully non-profit organization. Then we could divide the next Social Security surplus among the current recipients in individual accounts and completely privatize it as well.

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"I am a Tory Anarchist. I should like every one to go about doing just as he pleased- short of altering any of the things to which I have grown accustomed." (Max Beerbohm)

What is the benefit over government of a single over-sized private bureaucracy. Aside from the tax issue, that would for all intents and purposes be even more centralized and inefficient. Private sector efficiency requires competition. I don't think that can be done to easily with charity.
It seems like it would do more to get people competative about giving. That would require strong consumer pressure to support charitable companies and avoid the noncharitable ones. If we prefer government incentive, we should up the rewards corporations receive for creating and contributing to useful charities.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside

In addition to the disincentive of high taxation and the problems caused by the national debt, government welfare is not as effective as private charities at identifying and providing for the needs of the poor. The government typically has a rigid structure that estimates when and where such needs will occur, often incorrectly. Private charities are far more flexible.

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"I am a Tory Anarchist. I should like every one to go about doing just as he pleased- short of altering any of the things to which I have grown accustomed." (Max Beerbohm)

but not if the private firm is a single oversized bureaucracy created by a government bureaucracy that has monopoly control and does too many different things. Might as well be government.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside

My theory is that it would gradually become less bureaucratic after it was privatized.

__________________
"I am a Tory Anarchist. I should like every one to go about doing just as he pleased- short of altering any of the things to which I have grown accustomed." (Max Beerbohm)

only if it is held accountable somehow. Private competition or government budget control. Otherwise bureaucrats will run the show and it will become even more Vogon.

__________________
"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside