WASHINGTON — House Ways and Means Committee Chairman Kevin Brady. R-Texas, on Wednesday suggested that his upcoming tax bill could force changes to 401(k) plans and other retirement accounts, a move that would buck a promise from President Trump that those accounts would be left alone.

The congressman, speaking at a breakfast hosted by the Christian Science Monitor, said, “We think in tax reform we can create incentives for people to save more and save sooner.”

Brady, who’s expected to introduce a tax bill next week, said he was “working very closely with the president” on the issue. He added that many people who have tax-incentivized retirement accounts contribute $200 per month or less, a level he thought was too low.

“We think we can do better,” Brady said. “We are continuing discussions with the president, all focused on saving more and saving sooner.”

Several hours later, Senate Finance Committee Chairman Orrin Hatch, R-Utah, also said he would oppose Trump’s vow to protect 401(k) plans but that he was open to changes if they made sense. “I’m open to look at anything,” Hatch said Wednesday morning. “I don’t have any problem looking at everything.”

He also said he doesn’t feel pressure to change the Senate’s eventual tax bill because of pressure from the White House. “No I don’t think so,” Hatch said. “He has his point of view, and he may prove to be right in the end. We’ll just have to see. But I’m open-minded about it.”

Hatch said he hasn’t spoken with Trump about the 401(k) issue since the president sent his directive about it Monday morning.

Trump on Wednesday told reporters “401(k)s are very important,” noting their benefits for the middle class. And while he praised Brady as “fantastic,” he said it was unwise to negotiate on any changes to the tax code’s treatment of retirement plans.

Hatch is the top tax writer in the Senate, and he and Brady have outsized influence over how the tax legislation comes together.

Economists and financial advisers often urge people to begin saving for retirement as soon as possible because investment savings compound and grow much faster when people start contributing to it at a younger age.

Brady wouldn’t go into any details about how he planned to change incentives to encourage more savings. Rather, he suggested that the current construct of 401(k) accounts and Individual Retirement Accounts was not working well.

These types of accounts allow people to contribute up to $18,000 a year pretax as a way to incentivize saving for retirement. Lowering the tax-free threshold could raise more revenue, but it could also rankle voters. In 2015, more than 50 million Americans had active 401(k) accounts.

Democrats quickly pounced. Sen. Ron Wyden, D-Ore., said Wednesday that 401(k) proposal was an example of Republican lawmakers working to eliminate middle-class tax benefits so they can cut tax rates for the wealthy.

“They cannot keep their hands off your 401(k),” Wyden said. “They can’t help themselves, and you bet we are going to take this to the mat. And they have clearly reopened once again this question of rolling back fundamental retirement protections for working-class people.”

Brady is planning to introduce his tax bill next week, which Republicans hope will lead to the most sweeping changes to the tax code in more than 30 years. But almost all the key details of the bill remain a mystery. Again and again on Wednesday, Brady said the most pressing decisions have not been reached.

For example, he said he hasn’t decided what income levels would merit certain tax rates or how many tax deductions to eliminate to partially offset the lower rates. He said he hasn’t decided whether to impose a top tax rate for the wealthiest Americans or whether the tax cuts would be retroactive to income earned in 2017.

He also wouldn’t say how the tax bill would affect the type of taxes paid by hedge fund managers, even though Trump has promised to eliminate their special preferences.

“In about a week, you will be able to see the reforms proposed and where we are heading with it,” Brady said. He said he couldn’t guarantee that every American would see their taxes go down because of the changes, but he could “guarantee that every American will be better off because of a simpler tax code that lowers those rates and improves their paychecks.”

This political caution is infuriating some Republicans, who feel that too many details are being kept secret too late in the process. Brady and Republican leaders want to pass the tax-cut bill by the end of the year, but some lawmakers are threatening to try to block a vote on a House budget resolution Thursday if they don’t have more details. A number of lawmakers from New York and New Jersey are concerned that the tax plan could eliminate the ability of people in their states to deduct state and local taxes from their federal taxable income.

Brady said Wednesday that discussions about state and local deductions are ongoing, and there was a meeting with concerned lawmakers Tuesday night. He said he was hopeful the issue will be resolved, but he did stop short of assuring reporters that the budget resolution would pass by Thursday. Republicans need to pass the budget resolution to ensure they can eventually pass a tax-cut bill without support from Democrats in the Senate.

Republican leaders were continuing to scramble Wednesday to mollify concerned members ahead of Thursday’s budget vote, and meetings were expected to continue throughout the day and evening.

But even if they resolve the issue of state and local taxes, the new flare-up over 401(k)s reveals how many difficult issues remain.

House Republicans are hopeful that Brady will be able to pass his bill by the end of November, moving the process over to the Senate. Brady said adjustments to his bill will likely be made continuously to build support.

Even though many details remain unresolved, the White House and Republican leaders are aiming to write tax bills that meet several key targets. They want to lower the top corporate tax rate from 35 percent to 20 percent, collapse the number of income brackets paid by families and individuals from seven to three, and eliminate the estate tax and the alternative minimum tax.

Democrats and a number of budget experts have said the Republican tax plan would predominantly benefit the wealthiest Americans, with some taxes actually going up on the middle class and upper-middle class. Brady dismissed these concerns, telling people to study the bill he introduces next week.

He said that after the tax cut measure becomes law, he will pivot his attention next year into dismantling the Internal Revenue Service through a process he described as a “bust up (of) the IRS as it is today.” He said he wants the focus of the changed agency to be “focused on that simpler, fairer tax code” that the bill would create.

The comments by Brady and Hatch show the immense pressure that congressional leaders are under to find new revenue to offset some of the sweeping tax cuts Trump has promised. The Tax Policy Center, a nonpartisan Washington think tank, has analyzed that Americans saved $67.2 billion in taxes by contributing to defined-contribution plans like 401(k) accounts in 2015. Some Republicans believe they need to eliminate at least $400 billion a year in tax deductions and incentives to ensure that their tax plan can pass the Senate according to certain rules.

If Brady is going to offer some Republicans major concessions on the state and local tax debate, he could be forced to seek new revenue elsewhere, and the retirement accounts appear to be one target.

Sen. Bob Corker, R-Tenn., said Wednesday that the White House should not be putting down markers about what will and won’t be in the bill. Instead, he said, the White House should give lawmakers room to negotiate because they will have to make difficult decisions. Corker said they will ultimately need to eliminate $4 trillion in tax benefits over 10 years, something he said will take a “herculean effort.”

“To begin telling them in advance what is on the table and off the table does nothing but hurt the effort,” said Corker, who has signaled he would eventually oppose the tax bill if it adds to the deficit.