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Rep. Kyrsten Sinema, Arizona Democrat, voted for the bill, yet urged her state’s insurance chief to implement Mr. Obama’s fix.

Reps. Lois Capps and Zoe Lofgren, California Democrats who voted against the House bill, made a similar plea to California Health and Human Services Secretary Diana Dooley.

(Corrected paragraph:) Early on, Sen. Bill Nelson, Florida Democrat, urged his state officials to implement Mr. Obama’s fix.

Four Republicans bucked their party and voted against the House bill, perhaps because it could be viewed as an attempt to smooth over Mr. Obama’s controversial reforms.

Meanwhile, the insurance industry is left to sort it all out.

“The question is what happens. Who will join the markets?” Karen Ignagni, CEO of America’s Health Insurance Plans, said on Fox. “Will it be the young and the healthy balancing out the old and the sick?”