You can't exactly force people morally to help the less fortunate. Personally, I think that a government of the people has the responsibility of protecting rights and liberties assigned to those people from infringement by other people, and pursuing the prevention of the great natural evils such as disease, starvation, etc. And also that it should work towards the goal of eliminating deficits of birth in less fortunate circumstances by enabling quality primary education for all, mandating adequate care for children, and subsidizing basic nutrition as needed.
All of those things I'd consider helping the less fortunate, and at least in that vision are accomplished by the collection of the tax dollar. My list of things that help the less fortunate is not complete, but I am in support of providing equality of opportunity. I could speak more on what that means later.
The view I present is sketchy and I'd like to refine it. How would such a government function and remain small to serve the main purpose of protecting the rights of the people? What role do non-government charities play and should they have a bigger one? Do I have a moral obligation to them? How to implement this for foreign people outside my society?
I'm not sure on all that and more. I'll have to talk to more people.
So in short, I think much of the true obligation itself may fall upon the organizing structure of society rather than the individual, but we as a population do have an obligation to help people survive and have reasonable opportunity.
If given the choice to spend a nebulous $500 on an Xbone for me or that $500 on medical care for a child my decision is clear. But how does that choice change if the money is earned by my work, or is $50,000 instead, and how far should I go looking for ways to help? It's tough to parse it out.