To outsiders Clint was the soft-hearted one. Natasha, with her icy exterior and her cool lethal dexterity, was not made of maternal stuff. But Clint knows that when Natasha says 'whatever it takes', he understands it to mean, 'whatever it takes to bring her home'. He knows that when Katniss left for her mission, it was her mother who watched her leave.
He also knows that the women in his family are made of stubborn stuff and they may very well be bringing Katniss home kicking and screaming.
Part I here