President Trump shot down a possible approach for raising revenue to finance tax cuts in politically must-do legislation for the Republicans, promising Monday the popular 401(k) retirement savings program will be untouched.

Still, the head of the House's tax-writing committee indicated that changes to the 401(k) structure may still be on the table as Republicans push an ambitious timetable to get tax legislation written. Asked about the issue, Ways and Means Committee Chair Rep. Kevin Brady (R) of Texas said: "I don't want to get ahead of the committee. That will all be part of the tax reform bill."

And in response to whether Mr. Trump's tweet changes in any way what the panel was planning to do, Mr. Brady replied only, "no."

Republicans are scrambling to find new revenue sources to pay for anticipated tax cuts exceeding $1 trillion. A proposal to eliminate the widely-used federal deduction for state and local taxes has run into heavy opposition from GOP House members from high-tax states, threatening the enactment of tax legislation that Republicans deem essential to retaining their majority in next year's elections.

Trump pledged in a tweet there will be "no change" to tax incentives for the 401(k) retirement programs.

The No. 2 Republican in the Senate, Majority Whip John Cornyn of Texas, said he's "sympathetic" to Trump's opposition to curbing 401(k)s because "we don't want to discourage people from saving."

But he cautioned against ruling out ideas at this stage of the legislative process. "I do think we need to be careful because there are going to be a lot of different trial balloons, and what counts is how you put all this together," Senator Cornyn said.

The plan crafted by Trump and Republican leaders calls for steep tax cuts for corporations and potentially individuals, a doubling of the standard deduction used by most Americans, shrinking the number of tax brackets from seven to three or four, and the repeal of inheritance taxes on multimillion-dollar estates. The child tax credit would be increased and the tax system would be simplified; most Americans would be able to file their income taxes on a postcard, according to the plan.

Crucial details of the plan have yet to be worked out, notably what income levels would fit with each tax bracket.

With the possibility of the state and local deduction being at least partly preserved, some Republican lawmakers were considering limiting the amount workers could save in 401(k) retirement accounts.

"It was a trial balloon and it crashed," said Brian Riedl, a senior fellow at the conservative Manhattan Institute. "They're struggling to find legitimate offsets" for tax cuts.

"Everyone has been promised they are going to be better off with tax reform and that's really hard to do in a fiscally responsible way," Mr. Riedl said.

Employees' earnings from defined-contribution retirement plans such as 401(k)s aren't taxed until retirement; pay-ins by both employers and employees also receive tax-preferred status. That cost the government $82.7 billion in lost revenue in the recent budget year ending Sept. 30, 2016 – a potentially juicy target for Republican tax-cutters.

With 55 million United States workers holding some $5 trillion in their 401(k) accounts, the plans have become a touchstone of retirement security for the middle class.

"This has always been a great and popular middle class tax break that works, and it stays!" Trump tweeted. "There will be NO change to your 401(k)."

Appearing with Ivanka Trump in Pennsylvania, US Treasurer Jovita Carranza echoed the president, telling the audience the retirement plans "will not be touched."

Rep. Diane Black (R) of Tennessee, the chairman of the House Budget Committee, said of the Trump-rejected proposal on retirement plans: "There are still some dials that do have to be turned. This is a major effort and when you dial one thing you have to look at another."

House Republicans will be working to pass a budget this week so they can turn their attention to the tax overhaul. Trump warned Sunday that action on tax reform is crucial to avoiding political failure in 2018. He'll work to rally support for the plan at the Capitol Tuesday at a lunch with Senate Republicans.

Trump personally implored House GOP members on a conference call to swiftly adopt the budget that was passed last week by the Senate, with the hope of clearing the way for what he described as historic tax cuts.

Trump told the lawmakers they were on the verge of doing something historic, according to one Republican official, who, like others, spoke on condition of anonymity because they were not authorized to discuss publicly what was intended as a private update for members.

Another GOP aide familiar with the conversation said Trump told the members again and again that the party would pay a steep price in next year's midterm elections if it failed to pass his plan.

The Senate last week passed a budget plan that includes rules that will allow Republicans to get tax legislation through the Senate without Democratic votes or fear of a Democratic filibuster. House Republicans signaled Friday they would simply accept the Senate plan to avoid any potential delay on the tax measure.

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Republicans are desperate to rack up a legislative win after a series of embarrassing failures despite the party controlling both chambers of Congress and the White House. Topping the list: their stalled attempts to pass legislation repealing and replacing "Obamacare." If tax overhaul legislation doesn't pass, many in the party fear a complete rout in 2018.

This story was reported by the Associated Press. AP Congressional Correspondent Erica Werner and AP writers Jill Colvin, Alan Fram, and Andrew Taylor contributed to this report.