The primary problem with private charity is that it is too unpredictable. If you went to a homeless shelter on Thanksgiving, you would think that the line to serve soup is usually longer than the line to receive soup. If you went to a homeless shelter on a Tuesday in February, you would find that there are suddenly not enough volunteers to man the shelter. The same problem can plague charitable relief for the homeless - you simply can't plan ahead when your only source of funding is donations. The government will need to be the principal actor in caring for the homeless (though charities can still be a worthwhile partner in helping the homeless get back on their feet).
I do not think that private charity is enough to cope with the needs of homeless people. I think that there are way too many logistical problems and issues to deal with if only private charities are used to handle the problem. I think that public donations are still need to help with the problem.
Private charity is not enough to cope with the needs of homeless people. Although it does help homeless people, if it were enough, we would not have any homeless people in the United States. Many homeless people need mental health care which is very expensive and very difficult for them to find. They do not want to be homeless but after awhile, they learn to survive on the streets. The government needs to do more to get these people the help that they need.
If private charities were enough to cope with the needs of homeless people, we would no longer have homeless people. Homelessness needs to be dealt with by taxation and powerful economies full of a lot of jobs, and affordable housing. To think charity can combat this is just simple foolishness.
The United States of America has a lot of private charities, but we also have a lot of homeless people. Therefore, I would say it is safe to say that private charity is not enough to cope with their needs. Obviously there is a lot of room for improvement, but I think it's going to take more than private charity.