Many homeless find themselves begging for any spare change you can spare. While you may not realize it, they're aware of how they look (and smell). They peer out into the crowd wondering who'd be a "kind soul." It isn't your rejection that hurts them most... It's how you shake your head without even speaking a word or acknowledging their existence. When you speed up to walk away after shaking your head no or choose to look away or pay attention to something else, like your phone, it's like you're dismissing the fact that they're human too. Of course, the opposite is also true in that when you say "Yes," you're acknowledging this humanity. What it all boils down to is the fact that the homeless yearn to be respected and treated as you'd treat any other human.
One way you can show them respect in this regard is by giving them time... Share a meal, sit down and talk to them like you'd talk to anyone else, or if you're in a hurry, look at them when you say "No." Time and respect are ways of showing them they're still human, even though they're down on their luck right now. This is something you'd do with the elderly, your family, and other people around you so why can't you do it for them? Why can't you let the light of Jesus shine through you? It doesn't take long to bless someone in this way today.