Media headlines commonly refer to the surge of unaccompanied children from Central America as "refugees." In fact, it's a precise term that's not easy to qualify for.
Even before getting to that, it is worth noting that many of the children do not legally qualify to be called "unaccompanied." I know that sounds weird, but to qualify you must not have legal status and you cannot have a parent in the United States. If your parent (with legal status or not) is already here, you are not unaccompanied even if you came alone.
Refugee status requires demonstrating persecution. From the Immigration and Nationality Act:
(42) The term "refugee" means:
(A) any person who is outside any country of such person's nationality or, in the case of a person having no nationality, is outside any country in which such person last habitually resided, and who is unable or unwilling to return to, and is unable or unwilling to avail himself or herself of the protection of, that country because of persecution or a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion, or
(B) in such circumstances as the President after appropriate consultation (as defined in section 207(e) of this Act) may specify, any person who is within the country of such person's nationality or, in the case of a person having no nationality, within the country in which such person is habitually residing, and who is persecuted or who has a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion. The term "refugee" does not include any person who ordered, incited, assisted, or otherwise participated in the persecution of any person on account of race, religion, nationality, membership in a particular social group, or political opinion. For purposes of determinations under this Act, a person who has been forced to abort a pregnancy or to undergo involuntary sterilization, or who has been persecuted for failure or refusal to undergo such a procedure or for other resistance to a coercive population control program, shall be deemed to have been persecuted on account of political opinion, and a person who has a well founded fear that he or she will be forced to undergo such a procedure or subject to persecution for such failure, refusal, or resistance shall be deemed to have a well founded fear of persecution on account of political opinion.
For the children, "persecution" seems to refer largely to being forced into gangs or suffering abuse from family members. Providing evidence of that is no easy matter. Plus, if you are a minor whose parents are in the United States, you are ineligible to seek asylum.
One study argues that 40% of children would have a valid claim of Special Immigrant Juvenile Status, which focuses specifically on parental abuse or abandonment. Not only does that exclude 60% (still tens of thousands of kids) but even those 40% aren't automatic--they need to make a convincing case. The only way these children can have any hope of staying is to have extensive legal assistance, which is not likely given the sheer numbers.
The bottom line, then, is that popular usage considers the children refugees whereas most of them will likely never actually legally qualify as such. The only way that could happen would be for President Obama to declare them refugees en masse, a la Cubans. It's very hard to see that happening in the current political climate. The number of children exceeds the normal amount of refugees typically accepted in a year (there were 58,000 in 2012) but the Mariel boatlift is an example where it got very high one year (207,000 in 1980) so there is precedent. There were also 130,000 in 1975 when the United States left Vietnam.
One final note on the political side. Bill Clinton attributed his gubernatorial loss in 1980 to the Carter administration's resettling of Cubans in Arkansas. The logistics of refugee resettlement are formidable.