WASHINGTON — As Donald J. Trump’s norm-busting presidency careened through two impeachments, his departure set the stage for lawmakers to impose new limits on executive power like the period after Watergate and the Vietnam War.

But nearly nine months after Mr. Trump left the White House, the legal rules that govern the presidency have yet to be tightened. Would-be reformers, sensing that the window for change might close soon, are preparing a major push — one the Biden White House is eyeing warily.

House Democrats plan this month to reintroduce a broad package of limits on executive power. The bill — a refinement to legislation introduced last year during the presidential campaign for political messaging purposes — will pull together many proposals percolating in congressional committees.

The bill is expected to cover nearly a dozen issues. Among them: It would make it harder for presidents to bestow pardons in briberylike contexts and to spend — or secretly freeze — funds contrary to congressional appropriations. It would speed up lawsuits over congressional subpoenas. And it would strengthen the Constitution’s ban on presidents taking “emoluments,” or payments, from foreigners.

Known as the Protecting Our Democracy Act, the bill will be introduced by Representative Adam B. Schiff, Democrat of California, who also sponsored its 2020 version. But it represents the work of lawmakers and staff members on multiple committees who have been speaking with the White House for months; Speaker Nancy Pelosi directed them to combine their efforts, aides said.

Acknowledging that he was “working with my House colleagues to introduce and advance that legislation in the next few weeks,” Mr. Schiff, in a statement, framed the bill as a response to Mr. Trump’s “many abuses of executive power.” If Congress fails to enact new guardrails, he warned, Mr. Trump’s conduct would serve as “a road map for future unscrupulous presidents to abuse their power and defeat the most fundamental of oversight efforts.”

The White House supports many of the ideas, according to people familiar with its talks with House Democrats. They include keeping the statute of limitations from expiring while presidents are in office and temporarily shielded from prosecution; enhancing whistle-blower protections; banning foreign elections assistance; and tightening limits on whom presidents can appoint to temporarily fill vacant positions that normally require Senate confirmation.

“The prior administration’s routine abuse of power and violation of longstanding norms posed a deep threat to our democracy,” said Chris Meagher, a White House spokesman. “We strongly support efforts to restore guardrails and breathe life back into those longstanding norms. We’re working with Congress to do that, and we’re also building that commitment into every single thing this administration does.”

But the White House has also expressed skepticism and objected to some of the proposals as going too far and intruding on presidents’ constitutional prerogatives, the people familiar with the discussions said.

On clemency, for example, the White House supports making clearer that a pardon can count as a “thing of value” in an illegal bribery scheme and that presidents cannot pardon themselves. But the White House is uncomfortable with a related proposal to require disclosing to Congress internal White House communications and Justice Department case files about clemency recipients.

Administration officials are also said to be concerned about proposals to give Congress logs of White House interactions with the Justice Department, and to bar presidents from firing inspectors general without a good cause.

And amid the possibility that Republicans may regain control of Congress in the 2022 midterm elections, the White House is reportedly skeptical of a proposal to give lawmakers a clearer right to sue the executive branch to enforce its subpoenas. It would also expedite court resolution of such lawsuits and make lower-ranking officials personally liable for paying any court-ordered fines for refusing to comply with a subpoena — even if it is at the president’s direction.

Those changes could render obsolete the norm of resolving interbranch disputes over information through compromise and accommodation, with litigation as a rare last resort. (Mr. Trump flouted that norm, vowing to stonewall “all” oversight subpoenas and running out the clock in court.)

It remains unclear whether the final bill will include many of the ideas the White House has raised concerns about. In June, Mr. Schiff told MSNBC that House Democrats were getting “some pushback from the administration” and said he hoped President Biden and his team would see that the priority should be ensuring that the system of checks and balances works.

“If that means making sure that Congress can do its oversight, that’s what needs to happen,” Mr. Schiff added. “So I hope we get movement from them, but I’m determined to push forward regardless.”

House Democrats are not the only White House allies urging the Biden team to accept new curbs. Among the outside advocates joining them is Bob Bauer, Mr. Biden’s personal lawyer.

Last year, Mr. Bauer, who was a White House counsel in the Obama administration, joined with Jack L. Goldsmith, a senior official in the Bush Justice Department, to write a book proposing dozens of curbs on executive power called “After Trump: Reconstructing the Presidency.” This week, the pair formed an organization called the Presidential Reform Project.

With funding from philanthropic foundations, they are hiring a bipartisan team to lobby Congress. On Wednesday, they sent two letters to Attorney General Merrick B. Garland urging him to take certain steps to protect the Justice Department from politicization and to rescind three Bush-era memos that “take an extreme, indefensible view of presidential war powers.”

“We have the time, but not much time, for progress on reform before midterm politics and then the 2024 election cycle makes it harder,” Mr. Bauer said. “It is critically important to move some reforms in the coming months to achieve momentum for this program.”

By framing the coming House bill as a rebuke of Mr. Trump, Mr. Schiff may risk deterring Republicans — especially amid rumblings that Mr. Trump may run again in 2024. The Senate’s filibuster rule means some Republican support would be necessary there.

But staff aides and advocates say the strategy will be different in the Senate. There, the ideas are likely to be broken up and attached to other bills that, with different casting, are seen as more likely to garner Republican support.

Most of the ideas predate the Trump presidency, said Danielle Brian, the executive director of the Project on Government Oversight, which has sought to improve protections for inspectors general and whistle-blowers.

“Many of these address fissures in our system that may have been made more obvious by Trump but were long there,” she said. “I know why Democrats want to frame this as a Trump accountability bill, but we have been pushing for nearly all of these reforms for decades.”

For example, the proposal to require disclosure to Congress of White House contacts with the Justice Department is salient now because Mr. Trump and his aides pressured prosecutors to investigate his political adversaries and former aides viewed as disloyal, and to raise baseless suspicions about the legitimacy of his 2020 election loss. But it echoes a bill that Senators Charles E. Grassley of Iowa and John Cornyn of Texas, both Republicans, voted for in 2007.

And an idea to curb a president’s power to declare a national emergency and unlock special standby powers — as Mr. Trump did to spend more taxpayer funds on a border wall than Congress was willing to approve — echoes legislation introduced in 2019 by Senator Mike Lee, Republican of Utah, with 18 other Republican co-sponsors.

“We know we have 19 Republicans already signed on to emergency powers reform,” said Elizabeth Gotein, a director of the Brennan Center for Justice’s Liberty and National Security Program. “It has broad bipartisan support — we know that. If anything, it’s going to be an issue of holding onto Democrats now that Biden is president.”

As a presidential candidate, Mr. Biden said in a survey of executive power that he would sign many types of post-Trump overhauls — but did not endorse new limits on emergency powers.

The push is not limited to Mr. Schiff’s bill. For example, Mr. Lee has teamed up with Senators Christopher S. Murphy, Democrat of Connecticut, and Bernie Sanders, independent of Vermont, on the National Security Powers Act, which would combine new limits on emergency powers with curbs on presidential war powers and arms sales.

And as part of an annual defense bill last week, the House Armed Services Committee approved a provision to transfer control of the District of Columbia’s National Guard from the president to the mayor. Mr. Trump had deployed the Guard against demonstrators during racial justice protests last year.

Adding to the push, the group Protect Democracy has hired a lobbying team led by a former Republican Senate aide to reach out to lawmakers in hope of building bipartisan support, said Soren Dayton, a policy advocate with the group who worked for several elected Republicans.

“The time is now and the window is closing,” Mr. Dayton said. “Many of these ideas have a history of bipartisan support. Progress so far is proof that Congress cares about the power of the legislative branch and the rule of law, but we’re going to learn if it cares enough.”