The effort is part of a huge spending measure that would fund day-to-day federal operations through September — and head off a potential government shutdown later this month.

The measure would leave in place automatic cuts of 5 percent to domestic agencies and 7.8 percent to the Pentagon ordered by President Barack Obama Friday night after months of battling with Republicans over the budget. But the House Republicans’ legislation would award the Defense and Veterans Affairs departments their detailed 2013 budgets while other agencies would be frozen at 2012 levels — and then bear the across-the-board cuts.

The impact of the new cuts was proving slow to reach the broader public as Obama convened the first Cabinet meeting of his second term to discuss next steps.

The Pentagon did say it would furlough thousands of military school teachers around the world and close commissaries an extra day each week. And Homeland Security Secretary Janet Napolitano said the spending cuts were causing delays in customs lines at airports including Los Angeles International and O’Hare International in Chicago.

Obama said he was continuing to seek out Republican partners to reach a deal to ease or head off the cuts, but there was no sign that a breakthrough was in the works to reverse them.

The new GOP funding measure is set to advance through the House on Wednesday. It’s aimed at preventing a government shutdown when a six-month spending bill passed last September runs out March 27.

The latest measure would provide an increase for military operations and maintenance efforts as well as veterans’ health programs but would put most the rest of the government on budget autopilot.

After accounting for the across-the-board cuts, domestic agencies would face reductions exceeding 5 percent when compared with last year. But Republicans would carve out a host of exemptions seeking to protect certain functions, including federal prisons and fire-fighting efforts in the West, and to provide new funding for embassy security and modernizing the U.S. nuclear arsenal. The FBI and the Border Patrol would be able to maintain current staffing levels and would not have to furlough employees.

The legislation would provide about $2 billion more than the current level to increase security at U.S. embassies and diplomatic missions worldwide. Last September, a terrorist attack on the U.S. diplomatic mission in Benghazi, Libya, killed Ambassador Chris Stevens and three other Americans.

A project to repair the Capitol Dome in Washington could stay on track, and NASA would be protected from the harshest effects of the automatic cuts, known in Washington as a sequester.

The across-the-board cuts would carve $85 billion in spending from the government’s $3.6 trillion budget for this year, concentrating the cuts in the approximately $1 trillion allocated to the day-to-day agency operating budgets set by Congress each year. Those so-called discretionary accounts received big boosts in the first two years of Obama’s presidency when Democrats controlled Congress but have borne the brunt of the cuts approved as Obama and Republicans have grappled over the budget.

Both Democrats and Republicans for months have warned the cuts are draconian and would slow the growth of the economy and cost hundreds of thousands of jobs. The nonpartisan Congressional Budget Office, for instance, says they would slow the economy by 0.6 percent and cost about 750,000 jobs.

Obama presided Monday over the first meeting of his new-look Cabinet in a sobering climate of fiscal belt-tightening, urging humane management of spending cuts for communities and families that are “going to be hurting.”

“We can manage through it,” the president told reporters. Obama and members of his Cabinet had been warning for weeks that the cuts would be painful, but the fact is they will be slow to take effect, with the first furloughs of government workers not due until next month. Cuts to many programs may go unnoticed entirely.

The White House budget office’s 83-page sequestration order was released Friday evening, detailing the cuts to more than 1,000 separate government accounts, big and small. Cuts of 7.8 percent that are set to strike defense accounts include $5.2 billion for construction at Army bases. Other accounts are far smaller, like $32 million to operate and maintain the St. Lawrence Seaway.

Each agency is supposed to apportion the cuts equally to each “program, project and activity” within the broader accounts, which gives agency heads some flexibility since it’s up to them to define what that means. And it’s not clear what recourse others would have if they disagreed with an agency’s choices.

“That leaves it pretty much to the administrators in the agency in which that account falls to determine how he’s planning on applying it,” said G. William Hoagland, a budget expert with the Bipartisan Policy Center. “I don’t know that anybody’s going to be held accountable if some administrator defines a project the way he wants to define it.”