NEWPORT NEWS, Va. (AP) — No progress to report in efforts to stave off looming government-wide spending cuts, President Barack Obama on Tuesday singled out for praise the few Republicans who say they're open to aspects of his approach, seeking to turn up the heat on GOP leaders ahead of Friday's deadline.

Obama rejected a proposal floated by Senate Republicans to give the president more flexibility to pick and choose which programs should be cut to reach the $85 billion over seven months mandated by the so-called sequester. "There's no smart way to do that," he said.

"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 added at a shipbuilding site in Virginia.

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 every week off without pay, but the furloughs won't start for a month due to notification requirements. That will give negotiators some breathing room to keep working on a deal.

The sequester was designed as an unpalatable fallback, meant to take effect only if a congressional super-committee failed to come up with at least $1 trillion in savings from benefit programs. Obama wants to replace the sequester with a package of targeted cuts and tax increases, while Republican leaders insist the savings should come from reduced spending alone.

With GOP leaders refusing to entertain the president's proposals, Obama turned to the few rank-and-file Republicans who have suggested they are open to solutions that include raising new revenues to replace some of the cuts.

"I've got to give Scott Rigell credit," Obama said, referring to the Virginia Republican who traveled with him on Air Force One to call attention to the need to find a way out of the looming cuts.

He acknowledged it was politically difficult for Republicans like Rigell to be seen with Obama, but said that he's part of a chorus of Republicans urging Congress to strike a deal. Obama also pointed to Virginia's Republican governor, Bob McDonnell, and to Sen. John McCain, who was set to discuss the sequester along with other topics later Tuesday in a meeting with Obama and Sen. Lindsey Graham, R-S.C.

"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."

Even that minor point of consensus seemed far removed from the sentiment on Capitol Hill, where Republican leaders criticized the president for taking his arguments outside Washington, instead of staying to work out a plan before the deadline.

"The president has been traveling all over the country, and today going down to Newport News, in order to use our military men and women as a prop in yet another campaign rally to support his tax hikes," said House Speaker John Boehner, R-Ohio.

At Newport News Shipbuilding, Virginia's largest industrial employer, Obama renewed his effort to warn of the dire consequences the cuts could have on military readiness and local economies. He spoke in front of a massive submarine propeller, with workmen and the few female employees watching up from the cavernous assembly floor and down along railings from three open levels above.

"The threat of these cuts has already forced the Navy to cancel the deployment and delay the repair of certain aircraft carriers," Obama said.

Mike Petters , president and CEO of factory parent company Huntington Ingalls, said in an interview that the company will probably "throttle back" plans to hire between 10,000 and 15,000 workers over the next five years because of the budget uncertainty. He said his biggest headache in running the business is the continuing resolution.

"Fundamentally how do you do next year's budget if you don't know what this year's is like? So there's a lot of turmoil there and a lot of confusion," he said. "And what we're telling the workforce is look, there's a lot of stuff moving around out there, please try not to get too distracted by that."

The Navy has already delayed a long-planned overhaul of the USS Abraham Lincoln at Newport News Shipbuilding as a result of the budget uncertainty, and other plans call for delaying the construction of other ships. In Virginia alone, the White House says, about 90,000 civilians working for the Defense Department would be furloughed for a cut of nearly $650 million in gross pay.

Echoing Obama's warnings about the military repercussion were the five members of the Joint Chiefs of Staff, who traveled to Capitol Hill to say the cuts could impart a serious blow to military readiness. Their appearance marked the fourth time in the last three weeks that top Pentagon leaders have testified before Congress about the cuts.