Republican officials said one possibility was to add across-the-board cuts to supplement the targeted reductions spelled out earlier in the day at a closed-door meeting for the rank and file.
The original plan targeting education and the environment, food safety and law enforcement presents a blunt challenge to President Barack Obama.
It calls for eliminating a high-speed rail program the administration has ticketed for a multibillion-dollar expansion and recommends ending federal support for the Corporation for Public Broadcasting, family planning services and AmeriCorps.
The government's principal nutrition program for pregnant women would be cut 6 percent below last year's level.
The proposal marks an initial attempt by newly empowered Republicans to cut spending and reduce the size of the federal government. Yet it sets the stage for weeks of political combat as Democrats seek to blunt the cuts while tea party-backed conservatives demand more of them.
Republicans are "keeping our pledge to the American people that we will cut spending," House Speaker John Boehner, R-Ohio, said after details were outlined for the rank and file at a closed-door meeting.
Preliminary details of the plan emerged just before Obama hosted Boehner and his two top lieutenants at a White House lunch.
Reacting mildly to the recommended cuts, White House press secretary Robert Gibbs cited a "broad agreement that we have to change the way Washington works, particularly as it relates to spending."
At the same time, Gibbs said, "We have to do so in a way that protects the important investments so that we can win the future," signaling the president will fight to protect his own priorities.
House Democratic leader Nancy Pelosi was more pointed. "The Republican plan will cost jobs, undercut American innovation and clean energy, jeopardize our safety by taking cops off the street and threaten investments in rebuilding America - at a time when our economy can least afford it," she said in a written statement.
But some conservatives told the Republican leadership at the closed-door meeting that they want deeper cuts to fulfill campaign pledges to reduce spending to levels in effect in 2008. Officials described the effort on condition of anonymity to discuss the private discussions.
Republicans withheld many of the details of their proposal, which officials said was undergoing final changes before legislation is filed.
Still unclear, officials said, is whether the draft measure will try to ban the Environmental Protection Agency from regulating greenhouse gases under the Clean Air Act. Alternatively, a prohibition to that effect could be added when the bill reaches the House floor next week.
Other GOP priorities, including a ban on using federal money to implement the new health care law, are expected to be added, as well.
According to material presented by Rep. Harold Rogers, R-Ky., chairman of the House Appropriations Committee, the cuts would stretch across a vast range of domestic programs, from the EPA to housing, the weather service, food safety and inspection and the U.S. Army Corps of Engineers. The Community Development Block Grant, which provides funding for municipalities, would also be cut.
The cuts Rogers outlined have the blessing of GOP leaders, who are trying to carry out the mandate of last fall's elections while remaining mindful of the political limits of reductions that would affect many millions of people.
Inside the closed-door meeting, several conservatives urged the leadership to produce $100 billion in savings, as the party promised in its "Pledge to America" campaign manifesto last fall.
"I'd rather do $100 billion in across-the-board cuts than $58 billion in selected cuts," Rep. Jeff Flake of Arizona said afterward.
"I haven't looked at the specifics on the list, but the grand total isn't sufficient for me," added Rep. John Campbell of California.
"I think we have to do more than that, both because of what we told people we're going to do but also, frankly, almost more importantly, because of the severity of the situation."
The deficit is projected to be a record $1.5 trillion for the current fiscal year, and the national debt is approaching $14 trillion. Both categories have swelled in recent years as the United States tries to recover from the worst recession since the 1930s.
At the same time, public anger over red ink helped give rise to the tea party and the election of 87 new House Republicans last fall, enough to return the party to a majority.
Yet Rogers warned against cutting too deeply, outlining the potential impact of doubling his recommended reductions.
The result would mean furloughs and layoffs for critical law enforcement personnel including the FBI and Drug Enforcement Administration, he said, according to descriptions of his remarks.
The Food and Drug Administration could be returned to funding levels in effect two decades ago, he said of potentially deeper cuts, and the Federal Aviation Administration would have to furlough all of its air traffic controllers for 41 days a year.
Any cuts eventually passed by the House would be incorporated into legislation needed to keep the government in routine operation after its current funding authority expires on March 4.
Republicans have said privately they are prepared to pass a series of stopgap funding bills, each one lasting a few days or so, to avoid a cut-off in funds that would trigger a government shutdown. It is not clear what, if any, spending cuts they would seek in drafting their shorter-term measures, and the possibility exists for a protracted struggle between the GOP and the White House on the issue over the next few weeks.
In all, the recommendations include cuts of $43 billion from domestic and foreign aid budgets compared with levels in place for the fiscal year that ended last Sept. 30.
Increases for the Pentagon, homeland security and veterans' programs offset part of the total, leaving about $35 billion in cuts.
Eliminating AmeriCorps - a signature initiative of President Bill Clinton - would save $373 million. Ending police hiring grants would save $298 million.
The federal subsidy for the Corporation for Public Broadcasting would be eliminated, saving $531 million.
Republicans calculated they were cutting $58 billion, the amount by which they want to reduce Obama's requests for the current fiscal year.
The list of cuts contains numerous winners and losers. The FBI would receive a 4 percent increase, while NASA would absorb a cut of less than 1 percent cut from current levels.
The $31 billion health research budget would be frozen at 2010 levels.