The House and Senate will need to compromise on multiple differences in order to craft a final bill that can pass both chambers. For one, they will need to decide how to treat the controversial corporate alternative minimum tax, which the House bill would eliminate but the Senate plan would keep.

They will also need to reach agreement on the amount of state and local tax deductions and mortgage interest deductions taxpayers can take. Members of Congress from high-tax blue states have pushed for broader state and local deductions.

The individual tax bracket structure and treatment of the estate tax, or so-called death tax, could also emerge as sticking points.

Republican leaders are also considering cutting the corporate tax rate to 22 percent, rather than the 20 percent corporate rate in the House and Senate bills, according to two senior Republican lawmakers who spoke to CNBC.

President Donald Trump has signaled that he could be open to the change, which would help the GOP to raise revenue to pay for other tax cuts in the bill.

Ylan Mui contributed reporting