Senate Republicans have unveiled a sweeping plan to overhaul the Medicaid program, with changes policy analysts warn could lead to even greater coverage losses and pain for hospital systems than the aggressive proposal passed by the House of Representatives last month.

WASHINGTON—Senate Republican leaders left members from both ends of the party unsatisfied with their version of President Trump’s “big, beautiful bill,” touching off a fast round of new negotiations to hit their self-imposed deadline of putting the bill on his desk by July 4.