Tension is emerging between Republicans over their tax reform plan, as they made progress this week by passing a budget in the House and advancing a budget out of the Senate Budget Committee.

Passing a budget is the first step in the tax reform sequence, because it unlocks the reconciliation procedure that will allow tax legislation to pass with only 51 votes in the Senate, bypassing the filibuster.

Republicans can shape the eventual tax legislation by writing specifics into the budget reconciliation instructions. Accordingly, many lawmakers weighed in this week for the first time on the plan, which had been dominated by the "Big Six" members of the administration and congressional leadership.

But Republicans are revealing a split between those concerned about tax cuts that might increase the deficit and Republicans who want to play the supply-side Santa Claus, legislating big tax cuts for companies, small businesses, families, and everyone and anyone else.

On one side, Senate Budget Committee member Sen. Bob Corker, who recently announced he wouldn't seek re-election, emphasized that he isn't interested in a tax bill that includes "one penny's worth of deficits."

The budget that the Senate passed included a Corker-negotiated provision effectively limiting any potential tax cut to $1.5 trillion, not including the impact on economic growth.

That constraint would prevent Republicans from loading up the tax bill with all the deep rate cuts and tax eliminations they want, and require them to offset revenue losses by closing loopholes and ending credits and deductions.

"If you're going to try to produce a product that matters and is real and is not just some short-term giveaway that doesn't really help solve our nation's fiscal issues, it's going to take a lot of work," Corker said.

Meanwhile, other senators sought to sway the conversation in the other direction.

"We need to embrace unapologetically that we're doing a tax cut," Texas Sen. Ted Cruz told a group at the Capitol Thursday.

Writing in Breitbart, Kentucky Sen. Rand Paul sided with Cruz. He explained that he wanted the biggest tax cut possible, but that he would settle simply for ensuring that no one sees a tax increase and that as "many people as possible should get a tax CUT."

One way to satisfy both sides would be to eliminate tax breaks that mostly benefit high-income earners to cut rates, while also ensuring that lower- and middle-income families get tax breaks via targeted credits.

Sens. Marco Rubio of Florida and Mike Lee of Utah have advocated doubling the child tax credit as part of the tax package and making the credit refundable against payroll taxes, so that even families with no income tax liability could get tax relief.

On Thursday, Rubio published an analysis showing that his version of the tax credit would yield tax relief for families along the spectrum, while the plan risked raising taxes on some if it were not included.

Sen. John Thune, the number-three Republican in the Senate, said that he would "love to double" the child tax credit, but that it would depend on "what we have space for" in the tax bill.

Republicans would have more fiscal space if they scaled back their ambitions for lowering rates, or gave up on other priorities, such as repealing the estate tax.

And they have more space to include provisions such as the larger child tax credit if they aggressively eliminate the existing deductions and credits that have been placed in the tax code over the years.

This week, though, revealed how difficult it will be to eliminate some of the bigger and more popular provisions.

Republicans in the Senate and House expressed reluctance about the plan to eliminate the deduction for state and local taxes, which would raise about $1.3 trillion over a decade.

In the House, a handful of blue-state Republicans voted against the fiscal 2018 budget resolution as a warning to leadership that they don't plan to go along with the elimination of the deduction, which disproportionately benefits their constituents.

"I voted against the budget resolution — which I've never done before — to send a signal that we're serious," said Rep. Peter King, who represents a Long Island district, according to the New York Post.

Speaking Friday on Fox Business, National Economic Council Director Gary Cohn struck a resolved attitude on eliminating the break, portraying it as a benefit to high-income earners that could be redirected to the middle class as part of tax reform.

"We've gotta level the playing field, we've gotta simplify the system, and we've gotta deliver a middle-income tax cut," Cohn said.

Nevertheless, he added that the administration aims to be "practical" in negotiating with Congress and that its only red lines are reducing the corporate tax rate and delivering a middle-class tax cut.

The Senate still has to pass its budget, which it aims to do when it returns in a week. Then, the House and Senate will have to find agreement on a final product. That means at least several more vote series in which major issues will get refined, before the committees even start drafting actual legislation.