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Before Mr. Smith introduced his legislation, debate over abortion services within the health care law focused largely on the Obama administration’s decision to require larger employers to cover contraceptives approved by the Food and Drug Administration, including morning-after pills that conservatives equate to abortion.

Republican lawmakers have said the contraceptive mandate reneges on promises Mr. Obama made to keep abortion services out of his signature health law — a compromise that pro-life Democrats such as Rep. Bart Stupak of Michigan sought as the president gathered crucial votes for his reforms.