Should undocumented aliens be entitled to health care?

Congress recently decided that undocumented aliens are ineligible for medical benefits under the 1966 Medicaid Act, overruling a judicial decision that would have required the federal government to reimburse states partially for the costs of providing free care. Is providing such care simply a matter of prudence and charity? Or do illegal aliens have strong moral claims to medical care that generate duties for hospitals and government agencies?