I guess I should try to tie many of the things I said together and answer the question you are probably getting ready to ask "Why do you think libertarian ideals are the best tool for the job in the US?" (although I wouldn't characterize me ideals as libertarian)
Population is the major factor. Remember what I said about people being selfish and charity is a form of personal profit? Claus asks why it works in the instances it does?
The "warm and fuzzy feeling" people get when helping others is greatly diminished when they don't get the pleasure of seeing it appreciated. Why do you think they send you a picture of some kid when you donate to one of those "adopt-a-foreign-child" charitys? Because they know that people want to make themselves feel good when they donate and they feel much better when they actually see where their money is going.
This is why most people will tell you they would rather donate to a local charity than a national one. This is why it is so easy to get $250 for a software upgrade in about four posts, then it would be to try to get $250 in a general skepticism fund. The people knew where there money was going, they will see the benefits.
Now, in a small country of say 5 million people, situated in a small geographic area, the sense of familiarity is still not gone. A person in Denmark can still feel good about their charity, because they can still see the good it is doing. They still feel a common bond with everyone in their country, they still all feel as neighbors. So helping out the neighbors still feels good.
In Japan, anyone that is Japanese is treated like they are family. In the US, most people believe in the quote "Good fences make good neighbors." We are so large and diverse, in both culture and geography, we no longer feel like "family". What does a person in NYC care about a person in the hills of West Virginia? Or a person in Alaska care about a person in MI? Other than both happening to live in the same country, they have nothing in common. By no means do they feel like neighbors. And they will definitly not see the benefit their money is doing for those people. Naturally, they are not going to get any personal profit from their charity, so they are not going to be too happy about it.
Because I believe people are inherently selfish, I feel the best way to deal with that is not force them against their nature. Let them be selfish. This doesn't mean that nobody will ever give to charity, it will mean they will give it where they will maximize thier own personal profit, into their own community.
In Denmark, the whole country may feel like a community, so running a welfare state may seem appealing to them. But other than a few polarizing instances in US, people in the US do not feel all of our countrymen are "neighbors".
And there is another downside to government welfare in a large populace. When welfare is giving from a familiar source, say neighbors or a community group, the people that receive this help see the people that are helping them. They "feel the love" this help is given with. They understand that it was given to them to help them out. And they feel appreciation for it.
When help is given from a nameless, faceless entity such as government, there is less appreciation. And there is less incentive to give back to those that helped you. If your neighbor comes over to give you a hand, you appreciate what he has done for you and you feel that as soon as you can, you will help him out or pay him back as soon as possible. But do most people in the US that receive help appreciate where it is coming from? Does it give them the incentive to give back as soon as they can? My answer is no, they don't. And it is mostly not their fault, because it is hard to see that the help they are getting is actually coming from everyone. Some people in this country think the government just prints up money and passes it out; they seriously can't understand the government gets its money from the people, so the money they get is coming from the people.
In a small population, it is still possible to see the faces behind the government, so they may not suffer from this effect. I am often asked "Why isn't there a splurge of 'Welfare Babies" in Sweden?", this is one answer. In a small population, it may still be possible to feel the social obligation you have to use the help to better yourself, because that is why your neighbors gave it to you. In the US, that just doesn't exist anymore. And you may ask "What social obligation?" The one that exists when you give money like this. If you gave money to your friend to pay his rent and he drank it all, would you be happy? If a friend gave you money to go to school, so you could get a decent job, wouldn't you feel obligated to your friend to go to school and get a good job? Would it be proper and ethical to drop or flunk out of school and waste that money?
And isn't that the concept of welfare? To help those that can't help themselves? For the ones that can never help themselves, then it is a grant. But for those that can help themselves, it is a grant with the social agreement that they will use that money to put themselves into a position to help themselves. When they don't do that, they fail that social argreement. In a small population, people may be able to still feel that social obligation, but in a large populace, it becomes impossible. It is such and impersonal process, there is no connection between the help and the people giving the help.
That's why I feel the best way to approach charity in the US is from a local, community level. This is where it is best applied, best used, best appreciated and sees the best returns. When people with faces are able to give to people with faces, everyone wins.
That is how I decided which tool to use in this situation.