Are Christians obligated to give to every homeless beggar they see?

You answered your own question by adding the second part, because you already sense it is not right to give money to every beggar you see; that is not possible and often not the right thing. Sometimes the best thing is to tell an able-bodied beggar to clean himself up and go look for work. Some of these street beggars, interviewed incognito, have said they make sixty to seventy thousand dollars a year from the sympathy of drivers, and some are even hired out by companies. But yes, a Christian is genuinely obligated to give to the poor. Jesus made it hard for the rich man, who walked away sad rather than give his money away, and in Matthew 25 he says, whatever you did to the least of my brethren you did to me. So anything over and above your own needs and reasonable savings should be ready for those who are truly in need and cannot help themselves. God sends those people to you to test whether you really believe, and when you meet someone who genuinely needs help, you are obligated to give in whatever way you can, even buying them food.