Newt has ridiculed Mitt's notion that illegal immigrants will self deport if there is no work for them here, no work because employers have to really check their status before hiring.
The example Newt gives of someone's grandmother not leaving is true enough, but not relevant. Grandmothers are not who keeps sneaking across our southern border.
People come here to improve their economic status, to work. If there is no work, such folk will stay home or return home without us shipping them there. Their economic opportunities will be greater at home than here.
Illegals have returned home during the current period of high unemployment. See an ABC News article about this argument.