As the administration issues dire warnings about the looming sequester, congressional Republicans are a plan to give the president more flexibility in imposing the $85 billion in cuts, which they say could protect the most vital programs, The New York Times reports.

The plan would shift some of the political cost to President Barack Obama, and is opposed by the administration, which said Monday that it would do little to soften the blow.

At the same time, prominent Republicans said Obama was overstating the potential damage of the $85 billion in governmentwide cuts to frighten the public.

"There is a responsible way to cut less than 3 percent of the federal budget. It's time for the president to show leadership," Louisiana Gov. Bobby Jindal told reporters after a meeting between the president and governors, Reuters reported. "The president needs to stop campaigning, stop trying to scare the American people."

Jindal's comments followed the president's plea for Republican and Democratic governors to press Congress to stop the cuts, telling them he was willing to compromise with Republican lawmakers.

Obama will meet leading Senate Republicans John McCain of Arizona and Lindsey Graham of South Carolina Tuesday to discuss immigration, but a McCain aide said the talks could also delve into efforts to halt the cuts.

“This is the chance to do the big deal,” Graham said on CNN. “I’m willing to raise revenue. I’m willing to raise $600 billion in new revenue if my Democratic friends would be willing to reform entitlements and we can fix sequestration together.”

Janet Napolitano, the secretary of homeland security, said the automatic cuts would leave the country less well guarded and less able to meet terrorist threats, and would inconvenience millions of travelers. Ken Salazar, the secretary of the interior, warned that campgrounds would close, forest firefighting efforts would be scaled back and fewer seasonal workers would be hired.

“There’s always a threat,” Napolitano said. “We are going to do everything we can to minimize that risk. But the sequester makes that very, very tough.”

Napolitano warned the cuts would increase delays at ports of entry into the United States for container cargo by "up to five days."

Average wait times at customs will increase "by as much as 50 percent," she added, with even longer delays at the busiest airports such as Newark, Los Angeles and New York's JFK where delays could double to "four hours or more."

"I'm not here to scare people, I'm here to inform," Napolitano said at a White House briefing. "Please don't yell at the customs officer or the TSA officer because the lines are long," she said. "The lines over the next few weeks are going to start to lengthen in some dramatic ways in parts of the country."

Seeking to shift responsibility for the cuts to Obama and to fend off critics, Republicans were expected to unveil legislation Tuesday that they said would mitigate some of the biggest concerns by letting agencies and departments cull programs that were long ago proved to be ineffective, while making sure critical federal functions like air traffic control and meat inspection are spared, the Times reported.

But White House budget officials are leery. If Congress grants the White House the authority to protect air traffic controllers, Border Patrol agents and national parks, the administration’s campaign to prod Congress could deflate. Furthermore, the White House would take on the responsibility of deciding which programs to protect and which to expose — and the political consequences resulting.