Congressional Republicans have been struggling for months to resolve one of the most vexing problems in their tortuous effort to replace the Affordable Care Act: What to do about the generous federal funding for states that broadened their Medicaid programs under the law, while not shortchanging the 19 states that balked at expansion?

Now, as the House begins to hone details of its legislative proposal, a possible compromise has emerged. It would temporarily keep federal dollars flowing to cover almost the entire cost of the roughly 11 million Americans who have gained Medicaid coverage but would block that enhanced funding for any new participants.

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