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House Republican leaders on Monday urged President Obama to "stop campaigning" and hunker down with Congress to find an alternative to the bludgeon of spending cuts set to hit Friday, saying now is not the time "for a road-show president."

The plea came as the president prepared to head Tuesday to Newport News, Va., a major military community, to highlight the impact of Pentagon cuts on a shipbuilding facility. Obama's Cabinet secretaries also continued to issue dire warnings about the impact of so-called sequestration if the $85 billion in cuts begin to take effect March 1.

House Speaker John Boehner and his deputies, emerging late Monday to field a few questions from the press, said the Virginia stop shows Obama is more interested in scoring political points than making a deal.

"This is not time for a road-show president," House Republican Whip Kevin McCarthy, R-Calif., said.

House Republican Leader Eric Cantor, R-Va., whose state Obama is visiting, repeatedly accused the president of offering a "false choice" -- between passing tax increases and allowing steep cuts to take effect. The president has blamed Republicans for holding up a deal, which under Obama's terms would include a mix of cuts and revenue increases through closing tax loopholes.

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Republicans suggest there's still time to replace the sequester with cuts -- not tax hikes -- that makes sense.

"If the president was serious, he'd sit down with (Senate Democratic Leader) Harry Reid and begin to address our problems," Boehner said.

Boehner was not backing off his insistence that it's the Senate's turn to act.

While Obama is taking heat for once again hitting the road, Reid earlier in the day affirmed that the Senate will consider two plans to avoid the sequester later in the week.

Democrats have a bill of their own that would blend tax hikes and spending cuts, along the lines of what Obama has recommended.

Republicans, meanwhile, reportedly are looking at trying to give the Obama administration more flexibility to spread the cuts around so they don't impact high-priority areas -- like border officials, food inspectors and air traffic controllers -- quite as much.

Some Republicans argue that the administration already has more flexibility than it admits, and is making the problem sound worse than it really is.

But White House Press Secretary Jay Carney on Monday dismissed the idea that offering the administration more flexibility would spare a lot of the budget pain.

"There's no way around it," Carney said. "(That kind of bill) can't be written, not with the size of these cuts, and the fact that they needed to be implemented in such a short period of time in this fiscal year."

The White House continued laying out in stark terms what the cuts would mean for government services, dispatching Homeland Security Secretary Janet Napolitano to warn of the implications for critical security functions.

"I don't think we can maintain the same level of security at all places around the country with sequester as without sequester," said Napolitano, adding that the impact would be "like a rolling ball. It will keep growing."

Napolitano focused in particular on the impact to the border, saying her agency would be forced to furlough 5,000 patrol agents. She tamped down the notion that budget cuts would make the nation more vulnerable to terrorism, but said the sequester would make it "awfully, awfully tough" to minimize that risk.

Also Monday, Interior Secretary Ken Salazar said visiting hours would be cut at all 398 national parks, just as they prepare for an influx of spring and summer visitors.

Elsewhere in the government, Defense Secretary Leon Panetta has said the cuts would harm the readiness of U.S. fighting forces. Transportation Secretary Ray LaHood said travelers could see delayed flights. Education Secretary Arne Duncan said 70,000 fewer children from low-income families would have access to Head Start programs. And furloughed meat inspectors could leave plants idled.

Obama, speaking Monday to a gathering of the nation's governors at the White House, again urged Congress to pass an alternative package.

"The longer these cuts are in place, the bigger the impact will become," Obama said, adding that the cuts could be turned off "with just a little bit of compromise."

The Associated Press contributed to this report.