By Lauren Fox, Phil Mattingly and Ashley Killough, CNN

(CNN) -- House Republicans are expected to push a major tax overhaul out of committee this week, but some members are still lobbying to make substantial changes to the once-in-a-generation bill.

The GOP has remained upbeat about its prospects to pass tax reform out of the House of Representatives and even members who are pushing to amend the bill say they've been pleased with House Ways and Means Committee Chairman Kevin Brady's reception to their concerns. But even the most optimistic lawmakers and aides acknowledge the most volatile landmines remain very much alive.

The way in which Brady threads the needle with GOP leadership on the outstanding issues will determine whether the legislative machine is queued up when the bill hits the floor next week.

"A lot of our guys are right on the edge of yes," one senior House GOP aide said, acknowledging that given the number of major changes proposed in the first overhaul of the US tax code in 31 years, it was a good place to be with an often restive -- and sometimes intractable -- group of 239 lawmakers. "But right on the edge of yes doesn't get you over the finish line."

Tax reform -- perhaps more so than many other legislative issues -- attracts a vast array of special interests clamoring to preserve particular slivers of the tax code and members admit they're feeling the heat from homeowner's groups frustrated with a cap on mortgage interest deduction, evangelical groups upset that the tax bill ends the adoption tax credit and other small business groups concerned about who now qualifies as a so-called pass-through entity that can take advantage of a lower tax rate.

While there is palpable optimism by committee members in public, it's a different story behind the scenes as delicate negotiations continue to unfold.

Republican leaders have tried to make the case to their members that they must look at the totality of the tax legislation and how it lowers rates across the board rather than fixating on any one credit or deduction that's on the chopping block, but that hasn't stopped members from at least making a case for changes before the bill heads to the floor for a vote.

Perhaps the most high-profile debate has been over the effort to nix the state and local tax deduction, commonly referred to as SALT on Capitol Hill. Nearly 30% of filers take advantage of the popular tax break, especially in high-tax states like New York and New Jersey.

But many Republican members from those states have joined with Democrats to forcefully condemn the elimination of SALT and protest the bill, saying it unfairly punishes their constituents who've relied on the deduction to help avoid double taxation.

In a compromise, Republican tax writers left the property tax deduction in place but with a cap of $10,000. While some of those New York and New Jersey lawmakers including Rep. Tom MacArthur, a New Jersey Republican, have showed signs of standing down on SALT, others have vowed to keep fighting.

"I'm opposed to the bill in its current form," New Jersey Republican Rep. Leonard Lance told CNN.

Another major issue that has emerged is the elimination of the adoption tax credit, a tax break that middle-income families have used for years and a credit that the conservative evangelical community has mobilized to preserve.

Arizona Rep. Trent Franks, the Republican chairman of the adoption caucus, said that a group of conservative members is working around the clock to ensure that the tax credit is put back in the bill. One option is for a member of the House Ways and Means committee to introduce an amendment to the bill in committee. So far, Republicans have just deferred to Brady to introduce amendments, but Franks says that could change if the members don't see progress on the adoption credit.

"They say there is no Republican amendments in the committee. There will be one if they don't deal with it. I feel confident of that," Franks said.

Repealing the adoption credit also struck a nerve with Rep. Mark Walker of North Carolina, who chairs the conservative Republican Study Committee.

"As a former pastor, I know the people that make up this wonderful act of generosity. These are not often wealthy people. These are middle class or lower income families who really count on that $13,000, $14,000 to be able to go and find that child," Walker said. "To me, this is something that needs to be put back in there."

Leadership has tried to remind members that reintroducing any tax credits or deductions back into the bill could make it harder to meet spending targets. For GOP leaders, the argument has been two-fold: the overall economic results from the plan carry more weight than individual deductions or benefits that sit on the cutting room floor and the political imperative of the moment, laid bare after months of legislative fits, starts and failures, has ripened the rationale for supporting something.

Republican are also wary of re-introducing a bunch of tax cuts back into the legislation that they say has gone a long way to lower rates across the board.

"One or two of those you can handle, but 20 you can't," said Rep. David Brat, a Virginia Republican who is a member of the House Freedom Caucus.

But an analysis by the Joint Committee on Taxation found one more potential problem for the GOP. While the analysis found that a large number of households would see a tax cut in the early years after the GOP tax plan was passed, eventually the benefits would begin to taper off. The analysis showed that by 2027, nearly 20% of people would see the tax burden increase.

Behind the scenes, Republicans are also still working through how the GOP bill deals with so-called pass through entities. Some Republicans worry that while the GOP is trying to simplify the tax code on the individual side so that taxpayers can file their taxes on a post card, the tax writers -- in an effort to stop the uber rich from bypassing the top tax rate -- have created a more complicated system to govern who qualifies as a pass-through business, which under the GOP plan are taxed at 25 percent, lower than the highest individual tax rate.

"There is a real issue with small businesses potentially paying a lot more under this plan than the current tax plan," said one GOP member on background.

Overall, however, members aligned with leadership are still confident the bill is moving in the right direction.

"They are working through them one at a time. The sense is more progress is being made so I think things are moving pretty well in committee," Rep. Tom Cole, a Republican from Oklahoma told CNN. "Brady has been very open to sit down and have serious talks with everyone so I don't see anything here that threatens passage, I just see a couple more knotty problems that have to be worked through."