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President Obama took his campaign to warn about looming spending cuts on the road Tuesday, using a Virginia shipyard as a backdrop to his message that Congress' failure to act will cost jobs.

But back in Washington, Republicans said the president's theatrics aren't doing any good -- and that the American people would be better served if Obama worked with Congress on a viable alternative.

"The spending cuts are going to happen and the option now for the president is, do you want to work for a different way for these savings to be achieved?" Sen. Roy Blunt, R-Mo., said. "And that's very doable."

Senate Republican Leader Mitch McConnell, R-Ky., said he'd be "happy" to give the Obama administration "more flexibility" to spread around the $85 billion in cuts how they'd like.

That idea is being pushed as part of a Republican-backed bill expected to get a vote later in the week, along with a Democratic bill.

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But after months of bickering over the automatic cuts, the two sides are still far apart, with the cuts set to take effect Friday.

Senate Democratic Leader Harry Reid downplayed the idea that giving the administration more flexibility would help. The White House has also brushed off that option. Democrats generally say the cuts are too steep, and should be replaced with a package that blends targeted cuts with tax increases.

Senior administration officials, in a briefing with reporters late Tuesday, acknowledged that the sequester's impact would not necessarily be felt immediately. But they expressed confidence that, as the cuts take effect over a period of weeks, Republicans would start to bend on their resistance to raising more revenue. House Republican aides called that characterization "wrong," suggesting the White House has very little leverage because Republicans generally want spending cuts.

Obama visited Virginia's largest industrial employer, Newport News Shipbuilding, to stress that the spending cuts would idle military resources like naval aircraft carriers. The president continued to warn about the impact of the cuts, saying that for the Newport News and Norfolk areas ships might not get built as a result.

"And that hurts your bottom line, that hurts this community," Obama said.

The president said he's not interested in playing the "blame game" but merely wants to solve the problem with Congress. "These cuts are wrong," he said, calling this the "dumb way" to cut the budget.

Echoing the president later in the day, Pentagon spokesman George Little said "this is stupid."

The White House has warned that the cuts could affect everything from commercial flights to classrooms to meat inspections. The cuts would slash domestic and defense spending, leading to furloughs for hundreds of thousands of workers.

Despite the grim outlook, both sides seem more focused on blaming each other than coming up with a deal. Obama urged Congress to compromise, but the last known conversation between Obama and Republican leaders was last week and there have been no in-person meetings between the parties this year.

As Obama highlighted the impact of looming spending cuts with his trip to a Virginia military community Tuesday, Republicans accused the president of using America's service members as a campaign "prop."

McConnell claimed the president was trying to sow a sense of chaos.

"Personally, I don't believe the world will end if the president's sequester takes effect," McConnell said. "But our country would be much better served if the Democrats who run Washington would get off the campaign trail and work with us to trim the budget in a more rational way."

McConnell suggested that despite Obama's warnings of "utter chaos," the government should be able to cut 2 percent of its budget "without inviting disaster."

Frustration showing through, House Speaker John Boehner also used salty language as he urged the Senate to act, arguing the House has passed two bills already to deal with the so-called sequester.

"We should not have to move a third bill before the Senate gets off their ass," he said.

On the other side, Reid said his party wants to work with Republicans on a "balanced" plan.

"But my Republican colleagues are standing in the way of a solution. They only want cuts and more cuts. They are willing to sacrifice three-quarters of a million jobs rather than ask multi-millionaires to pay a penny more," Reid said.

The Senate is expected to hold votes on a Democratic and a Republican plan on Thursday. But with the $85 billion in cuts set to start taking effect Friday, hope is diminishing that any compromise could be reached before then.

Some congressional leaders have recently indicated their willingness to let the cuts take effect and stay in place for weeks, if not longer. There is some breathing room for political settlement even after Friday's deadline comes and goes: Provisions are in place to preserve the most crucial services and furloughs of federal workers are at least a month away.

McConnell claimed the president has presented the country with two options: "Armageddon or a tax hike."

Echoing comments made by House Republicans a day earlier, he said this is a "false choice."

The Associated Press contributed to this report.