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Republican ambitions to overhaul the country’s tax code got a big boost this week after the House narrowly passed a budget blueprint – but lawmakers are now scrambling to bridge deep divides over contribution limits to 401(k) retirement accounts and the possible elimination of a popular tax break.

Thursday’s budget measure passed over protests from 20 Republicans including lawmakers from New York and New Jersey who fear the current deduction for state and local taxes will be sacrificed.

“This isn’t over,” Rep. Tom MacArthur, R-N.J., told reporters after the vote. “I am confident we’ll reach an agreement. And if we don’t, then I don’t see how we can move forward.”

Rep. Kevin Brady, R-Texas, chairman of the House Ways and Means Committee, said his committee would introduce the tax bill on Nov. 1 – the deadline for doing so – and start the markup process the following week.

The big question for Brady has been whether he'll back a drastic reduction for employees' pretax contributions to 401(k) retirement plans, which President Trump publicly opposed but Brady did not rule out earlier this week.

However, Brady on Friday seemed to soften his position, telling Fox News that Republicans want to increase those contributions.

“We want to increase the amount that you can give to your 401(k) or IRA – for 401(k)s up to $20,000 or more – and we want to create incentives,” he said.

Potential changes to the plans created an uproar last week after rumors surfaced that Republicans were considering a plan to slash pretax donation limits from $18,000 for most people to as low as $2,400.

While Brady seemed to shift course Friday saying he wants to raise the contribution caps, there's a catch. According to White House and Capitol Hill sources, Brady is looking at making the accounts more like Roth IRAs, where money is taxed when it’s put in but not when it’s removed.

So lawmakers still could seek to reduce the amount of pretax dollars that can be contributed -- even if they raise the cap for after-tax contributions.

Any such reductions are risky territory for Congress. The backlash to last week's reports was so brutal that Trump tweeted on Monday, “NO change to your 401(k). This has always been a great and popular middle class tax break that works, and it stays!”

Just two days later, Trump walked back his comments said he “may be willing to negotiate” with congressional Republicans on how much Americans can contribute to their retirement accounts.

His change of heart came on the same day Brady said 401(k)s were still on the table. Brady is one of the authors of the tax bill.

Tennessee Republican Diane Black, chairwoman of the House Budget Committee, told Fox News on Friday that the goal “is to make sure that people can keep money and put it away and save” but skirted the question on whether there would be changes to the current setup.

“I think that you’re going to see that when we come out with our plan people are going to be happy about the kinds of advantages they’ll have with saving,” she said.

The discussion over what tax breaks to curb is part of an ever-intensifying debate pitting Republican lawmakers against one another as well as Democrats on how to offset promised cuts to individual tax rates.

Another idea to generate revenue is the repeal of the state and local tax deduction, commonly referred to as SALT. Doing so would raise $1.3 trillion over a decade, according to an analysis from the Tax Policy Center. But the organization warns that eliminating the local property and income tax deduction “could affect the mix of revenue resources used by state and local governments and could lead to reductions in spending for programs and services.”

Nearly 30 percent of taxpayers currently deduct state and local taxes. Though the deduction disproportionately benefits people in high-tax states and localities, individuals in all states can claim it.

Though the plan would preserve the popular deduction for mortgage interest, lawmakers in New York, New Jersey and California, pushed back strongly.

House Minority Leader Nancy Pelosi, D-Calif., said Thursday that the plan to eliminate SALT would cause home values to fall by 10 percent and called it “a rip-off of the middle class.”

Pelosi’s home state is one of the high-tax states that would be most affected by the elimination of SALT.

But Black said House leaders are still working on ways to make lawmakers in high-tax states happy.

“That’s a dial we’re still trying to turn,” she told Fox News on Friday. “When you have a tax code that is this large, if you turn a dial one way and it affects something, somewhere over on the other side and so we’re still working with them.”

Fox News' Barnini Chakraborty and John Roberts contributed to this report.