Senate Republicans are taking Medicaid cuts even further than their House counterparts with legislation that targets hospital payments.

WASHINGTON—Senate Republicans’ plan to extract more savings from Medicaid as part of their revised tax and spending package triggered a backlash within the party, raising concerns that leaders could miss their self-imposed deadline of getting the bill to President Trump’s desk by July 4.

The proposals from Republicans keep in place the current $10,000 deduction of state and local taxes, called SALT, drawing quick blowback from GOP lawmakers from New York and other high-tax states.