They warn that tax bill compromises contain measures that increase government spending.
The bill will include “no changes” to popular 401(k) retirement plans, according to a House memo.
The GOP's tax reform proposal would also allow Congress to create a fourth rate for the highest earners.
Mixing and matching would prevent Senate Democrats from blocking tax legislation.
The plan would pay for middle-class tax cuts with a new top rate for those who make more than $5 million a year.
The health industry expects the Senate to be more receptive to lobbying than the House on Obamacare replacement.
“We’re at that conceptual stage right now,” House Speaker Paul Ryan said.
The president’s warning came a day after GOP leaders made several changes to their measure.
The border tax plan is running into strong opposition from the energy industry and retailers.
So far, the opponents of his plan are winning.