The dispersion may be part of why even communities where no shelters are proposed are up in arms.

The tidal wave of children crossing the border has reignited intense passions around the core question of whether immigrants are entitled to receive costly government benefits and services.

Massachusetts Governor Deval Patrick—referencing his faith in referring to the situation as “a humanitarian crisis”—has offered two possible locations as short-term shelters for 1,000 children.

Patrick received a letter of support signed by 21 lawmakers, but Mayor Judith Flanagan Kennedy of Lynn, Massachusetts, wasn’t one of them. Kennedy has complained that her city’s services have already been overwhelmed by an influx of immigrant children, telling Fox News that “over 1,000 not-native-born children,” primarily Guatemalan, have entered Lynn’s school system in the last four years, forcing her to increase school budgets 9.3 percent and to cut other city budgets from 2 percent to 5 percent.

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“Education and health systems are already overloaded,” said Steven Camarota, director of research at the conservative Center for Immigration Studies. He said that a large fraction of these kids have special needs—related to language, trauma and low-income backgrounds—that will add to the cost. But, he added, “it’s not just cost that matters. It’s competition for scarce public resources. And part of the resentment is about the laxity, having an open border and an administration bent on releasing everybody and not focused on enforcement.”

Asked to comment on Kennedy’s remarks at the mid-July event, Patrick reiterated the importance of thinking of this issue in terms of families.

The complete economic picture requires a broader perspective than provided by those isolated on the cost or humanitarian side of the debate.

“Child migration will affect certain states and localities differently, based on where costs such as education are incurred but also based on gains in terms of spending for things like shelter and transportation,” said Michelle Mittelstadt of the Migration Policy Institute. Long-term economic benefits of immigrants entering the workforce should also be considered, she said.

Though immigration may strain some local budgets in the short term, costs and benefits tend to balance out in the end, said Alex Nowrasteh, immigration policy analyst at the Cato Institute, a libertarian think tank. “We all pay taxes and receive government benefits,” Nowrasteh said. “What we see again and again is that the fiscal cost of immigrants over time is about the same as it is for American citizens, which in the long run is about zero.”

—By Robin Micheli, special to CNBC.com