Making Health Care Available for Low-Income Workers Act of 2003 - Directs the Secretary of Health and Human Services to provide grants to States for demonstration programs to reduce the premiums for health benefits coverage under group health plans for individuals: (1) who are eligible for benefits under a State's Medicaid (title XIX of the Social Security Act) program (or, at the State's option, who would be so eligible but for their eligibility or coverage under a group health plan); and (2) whose income does not exceed 185 percent of the income official poverty line applicable to a family of the size involved.