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.

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 Senate Finance Committee, which oversees changes made to taxes and social safety net programs like Medicare and Medicaid,