Only two states say their National Guard operations could provide facilities to house unaccompanied immigrant children following a request for options from the government.
California said it has the facilities while Virginia said it would be willing to build them to meet federal requirements.
Both states told the National Guard Bureau they would require additional funding if asked to meet those requirements.
Most states say they aren't set up to handle that kind of housing or they lack the facilities.
Ohio also says it's concerned about government oversight of the program, pointing to a case of labor trafficking at a large egg farm in the state earlier this year.
Ohio Gov. John Kasich questions why unaccompanied immigrant children were released to sponsors allegedly involved in trafficking.