Hundreds of billions of dollars and the well-being of millions of people will be at stake when more states consider in coming months whether to expand Medicaid under the federal health care overhaul. As legislatures look ahead to their 2013 sessions, the calculating and the lobbying have already begun.

President Obama’s law expands Medicaid, the federal-state health program for low-income people, but cost-wary states must decide whether to take the deal.