In a week in which Germany has confronted international criticism for a hard line on debt-mired Greece, Merkel was hit with fresh accusations of coldness, just as others leapt to her defence.
Merkel was attending a public discussion with teenagers in the northern city of Rostock as part of a government-initiated series called "Living Well in Germany".
As seen in the video broadcast on public television, the Palestinian girl named Reem told Merkel that her family had been informed they would have to return to a camp in Lebanon imminently only to receive a last-minute temporary residence permit for Germany.
"It's really very hard to watch how other people can enjoy life and you yourself can't ... I don't know what my future will bring."
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Merkel expressed sympathy before defending her government's asylum policies.
"Politics can be tough," she said.
"You are an extremely nice person but you also know that there are thousands and thousands of people in Palestinian refugee camps in Lebanon."
She added that Germany would be unable to shoulder the burden of all the people fleeing war and poverty who would like to move to Europe's top economy seeking a better life.