(CNN) Republicans are well on their way to overhauling the tax code, but party schisms, red lines and inevitable local interests are already coming into sharp view.

Last week, the Senate and the House took the first steps on tax reform. The House passed its budget on the House floor while the Senate moved its own version out of committee, a crucial step in unlocking the GOP's ability to use reconciliation for tax reform; that process allows the Senate to pass its package with only 51 votes.

But almost two weeks after the GOP unveiled its framework for tax reform, the party is already grappling with the inevitable reality that for every tiny change leaders seek, a constituency is waiting in the wings to fight for or against it.

"People have become familiar with this code, they know how it works and when Congress is going to go in and change it, they are unsure if that change will work for them," said Sen. Mike Crapo, a Republican from Idaho and the Chairman of the Senate banking committee.

In the Senate, a thin margin

Fresh off the loss on health care, there is also concern that GOP leaders have no room for error as they attempt to get a long-awaited legislative win. Using reconciliation, Republicans don't need Democratic votes, but they'll need all but two members to be on board, something that rank-and-file Republicans recognize is a liability for them.

Already, Sen. Bob Corker, a Republican from Tennessee, has said he doesn't want the tax package to add to the deficit, a fiscal hard line that may be tough to comply with and will force the party into a place where it has to make serious tradeoffs in tax policy. Corker predicts that the party will need to find roughly "$4 trillion in loopholes that have to be closed." While many conservatives have argued that tax cuts spur economic growth that will offset the loss of revenue, Corker argues that he thinks the party needs to be realistic about how much growth to expect.

"I want to make sure this doesn't add one penny to the deficit," Corker said.

Corker also once again found himself publicly fighting with President Donald Trump over the weekend. And while this most recent spat between the two high-profile Republicans just barely touched the tax reform issue, it's difficult for the party to envision such legislation advancing without Corker's support.

"Bob Corker gave us the Iran Deal, & that's about it. We need HealthCare, we need Tax Cuts/Reform, we need people that can get the job done!" Trump tweeted Sunday evening

Bob Corker gave us the Iran Deal, & that's about it. We need HealthCare, we need Tax Cuts/Reform, we need people that can get the job done! — Donald J. Trump (@realDonaldTrump) October 8, 2017

Another Republican senator, Rand Paul of Kentucky, who became a "no" vote on the GOP's last version to repeal Obamacare, has also signaled his concerns with the current plan. In an op-ed in Breitbart , Paul argued that the GOP's framework cuts taxes for wealthy earners and the poor, but doesn't do enough to cut taxes for the middle class.

"I don't want to vote for a plan that cuts some taxes but raises them on others, especially not on the middle class. So I want everyone to see the errors in their plan, look for solutions, and come together for a plan that can pass," Paul warned.

The House deals with deductions

In the House, another piece of the tax framework has come under fire: the eradication of the state and local deduction . The deduction allows people to write off local and state tax levies on their federal returns, and Northeast Republicans in Congress -- many of whom have constituents who pay higher local and state taxes in states like New Jersey and New York -- want to preserve it at least in some form. Last week, Ways and Means Committee Chairman Kevin Brady and a handful of House GOP members dined at Ruth's Chris Steak House to discuss concerns over losing the deduction.

New York Rep. Chris Collins, a Republican, told reporters that discussions are ongoing about ways to at the very least preserve a piece of it, but the balance is delicate. Collins has suggested that taxpayers could pick between taking the state and local deduction or the mortgage interest deduction on homes valued at less than $1 million. But, the fact remains that at some point, Republicans will have to eliminate deductions in the tax code in order to pay for their other tax cuts. Axing the state and local deduction is estimated to raise $1 trillion in revenue for the GOP's tax plan.

The fear from GOP leaders is compromising on revenue raisers now only makes the rest of the process harder later. Not to mention, finding another $1 trillion isn't easy.

"I think every one of these are going to be hard," said GOP Sen. John Thune of South Dakota. "None of this is easy. ... I think right now our members need to just keep an open mind and keep things on the table and then at some point, when we really get into the nuts and bolts of this, we'll have to start making some decisions. But if you start saying now, 'I am not going to be for this or for that,' then you start getting into that slippery slope where every deduction becomes something that people want to save."

Republican rank-and-file members desperate for a win on tax reform say that their colleagues need to keep their eyes on the ball. The GOP needs to reform the tax code or face a rough 2018 midterm election when donors and the base will wonder what the Republican Party has accomplished in Washington where they control the Executive and Legislative Branch of federal government.

Republican Sen. John Kennedy of Louisiana offered this preview: "I think once (we're) finished, some people are going to be happy and other people are going to be sad, but that's what you do when you reform the tax code."