Controlling (defending) our border is a basic right of nationhood. The problems we face with Central American minors crossing into America through Mexico is a political crisis caused by Obama administration policies and statements, and not a refugee crisis obliging us to keep all those crossing into our country.
If the Central Americans are refugees from conditions that legally justify refugee status, Mexico, as the first country of refuge for those Central Americans, has the obligation--as is generally accepted--to rescue the refugees and not pass them on through to America.
Whatever you may think of that policy, the reason we intercepted Haitian refugees at sea and took them to refugee camps at Guanatanamo Bay, Cuba, was to avoid the legal responsibilities of refugees touching down on our soil.
If those kids are refugees, Mexico has the responsibility to host them.
UPDATE: Ah, a longer post on exactly this issue.