In the Senate Budget Committee, a dispute over whether the tax cuts should add to the deficit or be financed elsewhere in the budget was postponed by Senators Pat Toomey of Pennsylvania and Bob Corker of Tennessee until a final tax bill is released. The committee’s budget would allow $1.5 trillion in tax cuts, though Corker says he won’t back tax cuts that add to the deficit once economic growth is factored in.

Republicans skirmished this week over whether to eliminate the state and local tax deduction -- which would amount to a trillion-dollar tax increase mostly affecting blue states including New York, California and Massachusetts. The extra money is meant to offset lower individual rates and a higher standard deduction, but Republican House members from high-tax states are seeking to lessen the tax increase on their constituents.

“It’s ironclad that you will not see a full repeal," said Republican Representative Chris Collins of New York. "There will be an accommodation.”

Deficit hawks are pushing back, including Corker.

Corker ‘Disheartened’

"I’m disheartened right now,” Corker said of the effort to keep the state and local tax deduction. “All I see is a bunch of sugar being thrown on the table, but no one wants to eat even one leaf of spinach yet.”

The conservative group Heritage Action’s chief executive officer, Michael Needham, said in a statement, “It did not take long for Washington’s swamp creatures to begin picking apart Republicans’ sweeping tax reform proposal.”

House Ways and Means Chairman Kevin Brady of Texas said this week that he was “listening very carefully to lawmakers, especially from high-tax states.” Possible compromises would limit the deduction for top earners or allow people to claim either the mortgage-interest deduction or the state and local tax deduction.

Because the state and local tax deduction "is more than a trillion dollars and of its value as an offset, it is important to our overall effort, but there are lots of them. None of this is easy," Thune said.

Members of the Republican Study Committee of House conservatives raised a potential further complication Tuesday by calling for more generous tax cuts -- possibly cuts in capital gains and dividend taxes and expanding businesses’ ability to fully expense investments.