“This heartless spending plan attempts to balance the budget on the backs of the American middle class and would make life much harder for families and seniors,” said Senator Al Franken, Democrat of Minnesota. He predicted that if passed, it “would likely send our country into an economic free fall.”

The budget plan submitted by Mr. Mulvaney is reminiscent of the conservative House budget alternatives written by the Republican Study Committee, the group he belonged to before defecting to form the even more conservative House Freedom Caucus. Those budgets were routinely rejected by Democrats and significant numbers of Republicans, and were seen more as ideological documents than fiscal plans. Now Mr. Mulvaney is writing budgets for the White House.

Republicans were virtually unanimous in their estimation that Mr. Trump’s plan would be heavily rewritten. The health care debate has reminded many congressional Republicans that large numbers of their constituents facing tough economic conditions rely on Medicaid and other federal support programs. They know cutting too deep could have hurt them in the 2018 midterms. And nearly $50 billion in proposed cuts to agriculture over the next decade immediately set off alarms with farm-state Republicans who thought their Trump-embracing constituents deserved better.

In a joint statement, Senator Pat Roberts of Kansas and Representative Mike Conaway of Texas, the Republican chairmen of the Senate and House Agriculture Committees, said they would “fight to ensure farmers have a strong safety net so this key segment of our economy can weather current hard times.” But they left the door open to cuts in food stamp programs managed by the Agriculture Department.

This is the quandary for many Republicans: They are all for reining in spending but want to make certain that their home-state priorities are walled off. For each Republican worried about farm subsidies, there are others who do not like the sound of less money for health research, the State Department, transit projects and popular programs like Head Start.