The first bill would cost $95 billion and would extend unemployment insurance and expired tax breaks and be offset by the foreign tax and carried interest provisions in the original bill.
The second bill would extend the "doc fix," a term that refers to delaying a cut in Medicare reimbursements to doctors.
Votes are likely on both pieces sometime Friday, lawmakers said tonight.
COBRA health insurance and the federal medical assistance percentage under Medicaid would not longer be a part of either package but would probably come up after the Memorial Day recess for a separate vote.
The House Rules Committee may have to clear the bills before they can go to the floor.
Lauren Victoria Burke contributed to this story.
This story was updated at 7:15 p.m.