Three days out and no closer to any agreement, both parties sought to saddle the other with the blame for the painful ramification of the across-the-board cuts set to kick in Friday. Obama accused Republicans of steadfastly refusing to compromise, while the top Senate Republican, Mitch McConnell, chided Obama’s effort to “fan the flames of catastrophe.”

McConnell and other top Republicans were lining up behind a plan that wouldn’t replace the cuts but would give Obama’s agency heads, such as incoming Defense Secretary Chuck Hagel, greater discretion in distributing the cuts. The idea is that money could be transferred from lower-priority accounts to others that fund air traffic control or meat inspection.

But Obama, appearing at a Virginia shipbuilding site that he said would sit idle should the cuts go through, rejected the idea, saying there’s no smart way to cut such a large chunk from the budget over just seven months — the amount of time left in the fiscal year.

“You don’t want to have to choose between, ‘let’s see, do I close funding for the disabled kid, or the poor kid? Do I close this Navy shipyard or some other one?’” Obama said. “You can’t gloss over the pain and the impact it’s going to have on the economy.”

Giving the Obama administration more authority could take pressure off of Congress to address the sequester. But the White House is also keenly aware that it would give Republicans an opening to blame Obama, instead of themselves, for every unpopular cut he makes.

Not all Republicans were on board, either.

“We’ll say, ‘Mr. President, it is now up to you to find this $85 billion in savings,’ and we’ll say it’s to make it easier for you, but every decision he’ll make, we’ll criticize,” acknowledged Sen. Lindsey Graham of South Carolina in a CNN interview Monday.

The White House has warned the $85 billion in cuts could affect everything from commercial flights to classrooms to meat inspections. The cuts would slash domestic and defense spending, leading to forced unpaid days off for hundreds of thousands of workers.

The impact won’t be immediate. Federal workers would be notified next week that they will have to take up to a day off every week without pay, but the furloughs won’t start for a month due to notification requirements. That will give negotiators some breathing room to work on a deal.

Although Obama was to discuss the cuts among other topics Tuesday in a White House meeting with Graham and GOP Sen. John McCain, there were no indications that negotiations between Obama and congressional leaders were under way. Dampening hopes for a compromise was a key disagreement about whether new tax revenue, by way of closing loopholes and deductions, should be included in any deal, as Obama has insisted.

In the Republican-controlled House, Speaker John Boehner of Ohio said he’d already done his part, complaining that the House twice passed bills to replace the cuts with more targeted reductions.

“We should not have to move a third bill before the Senate gets off their ass and begins to do something,” Boehner told reporters.

Senate Democrats have prepared a measure that would forestall the automatic cuts through the end of the year, replacing them with longer-term cuts to the Pentagon and cash payments to farmers, and by installing a minimum 30 percent tax rate on income exceeding $1 million. But that plan is virtually certain to be toppled by a GOP-led filibuster vote later this week.

Recharging his effort to lay out the stark consequences for letting the cuts take effect, Obama traveled Tuesday to eastern Virginia, where he warned that workers at the state’s largest industrial employer, Newport News Shipbuilding, would sit idle. He stood in front of a massive submarine propeller, with workmen and the few female employees watching up from the cavernous assembly floor and said the cuts would mean construction and repair of Navy ships would be delayed or canceled altogether.

“These cuts are wrong. They’re not smart, they’re not fair. They’re a self-inflicted wound that doesn’t have to happen,” Obama said.

The highly staged visit earned him a harsh rebuke from Republicans, including Boehner, who claimed Obama was using U.S. troops as props in his campaign to scare Americans into raising taxes.

But Obama, grasping eagerly for the chance to portray his positions as having broad appeal, singled out for praise the few Republicans who say they’re open to new revenues as part of a deal. At the top of his list was Virginia Rep. Scott Rigell, who traveled with the president on Air Force One to call attention to the need to find a way out of the cuts.

“I boarded the plane knowing that some would potentially misinterpret this,” said Rigell, who both criticized Obama for not putting forward a detailed plan and criticized Republicans who say there’s no room to raise revenue or that the sequester should go into effect. “Even if you hold the view that defense spending should come down, this is not the right way to do it.”

Also on Tuesday came word of the first tangible impact of the looming budget cuts on the nation’s security at home. To save costs, the Department of Homeland Security has started releasing illegal immigrants being held in immigration jails across the country, Immigration and Customs Enforcement said.