Republicans on Monday rejected President Obama’s high-pressure push to avert a series of budget cuts called the sequester, saying that Obama is engaged in scare tactics and political campaigning when he should be seeking a deal.

“This is not time for a road-show president,” Majority Whip Kevin McCarthy (Calif.) said at a news conference with other House Republicans. “This is time to look for someone who will lead and work with us, because we’re willing to work with them to solve America’s problems.”

The lawmakers criticized Obama for a planned trip Tuesday to Newport News, Va., where he will highlight the impact of the cuts on the military-driven local economy.

A trio of GOP governors also said Obama is hyping the problem.

“I think he’s trying to scare the American people,” said Louisiana Gov. Bobby Jindal.

Understanding the sequester

With just days left before $1.2 trillion in budget cuts begin to take effect, that argument was the closest thing to progress Monday. There was a new round of grim political theater — including new warnings from Cabinet secretaries about the potential impact of the cuts — but no deal or substantive negotiations.

New Post-Pew poll

A new Washington Post-Pew Research poll shows that the standoff has risks for both sides, but more so for the GOP. Among respondents, 45 percent said they would blame Republicans if the cuts took effect and 32 percent said they would blame Obama. An additional 13 percent said they would blame both sides equally.

Obama has insisted that any sequester replacement must balance spending cuts with new measures to raise tax revenue. Republicans have insisted that it should not. On Monday, Obama urged a visiting group of governors to lobby their congressional delegations.

“Here’s the thing — these cuts do not have to happen,” he told the gathering. “Congress can turn them off any time with just a little bit of compromise.”

The sequester is a package of spending cuts worth $85 billion for the current fiscal year and $1.2 trillion over the next decade. It was designed as a poison pill, not a real-world policy. The idea, back in 2011, was that broad cuts would be so unappealing that Washington lawmakers would be motivated to replace them with new and less-disruptive reductions.

“I don’t think the public realizes how stupid these cuts are,” Sen. Mark R. Warner (D-Va.) said in an interview Monday with “CBS This Morning.”

“Limping from one budget crisis to another doesn’t do anything for this economy,” he added.

One reason for the lack of progress is that, on Capitol Hill, the deadline doesn’t quite feel like a deadline. In other recent budget showdowns, such as the debt-ceiling fight in 2011 and the “fiscal cliff” crisis this winter, there were hard deadlines with immediate, unpleasant consequences. Miss them, and Congress risked a national default or large tax hikes.

This deadline is different. Even if the sequester takes effect as scheduled Friday, it could be weeks before the first employees are furloughed and the first effects are felt by the public. That could leave plenty of time for Congress to reverse or modify the cuts.

On Monday, however, the administration continued its efforts to create a sense of urgency by laying out a vision of the sequester’s unpleasant effects.

Homeland Security Secretary Janet Napolitano warned that her agency would be forced to furlough 5,000 border agents as a result of the mandatory spending cuts. She said that probably would allow more illegal immigrants to enter the country and potentially compromise national security.

Napolitano said the reductions also would disrupt her department’s ability to conduct customs inspections at ports, leading to increased wait times for travelers and cargo shipments. She said disaster relief funding would be reduced by $1 billion, meaning aid for victims of Hurricane Sandy and tornadoes in Joplin, Mo., and Tuscaloosa, Ala., could be cut.

“I’m not here to scare people. I’m here to inform, and also to let people begin to plan,” Napolitano said. “Because they’re going to see these impacts in their everyday lives.”

At national parks, the effects could include shorter visitor hours, furloughs for paid staff members and less money for snow plowing.

That could delay spring openings at Yellowstone National Park and other places where snow must be cleared beforehand, according to Interior Secretary Ken Salazar.

At the National Institutes of Health, Director Francis S. Collins said the sequester would mean $1.6 billion in cuts and slow research on diseases such as cancer, influenza and Alzheimer’s.

Hundreds of research grants would go unfunded, he said, and some 20,000 highly skilled workers would lose their jobs. Collins said he also expects to have to turn away patients from NIH’s clinical center, which allows people who have exhausted their treatment options to participate in clinical trials.

At the Food and Drug Administration, officials said the cuts would probably mean delays in translating new science and technology into regulatory policy and decision making. That, they said, could result in longer wait times for the approval of new drugs and medical devices.

Senate bills expected

The warnings produced little progress on Capitol Hill, where Democrats and Republicans in the Senate are expected to introduce separate bills that would — in theory — avert the sequester. But both will be heavily partisan and designed to fail in hopes of embarrassing the other side.

For Democrats, the plan would be to delay the sequester until January and pay for it by cutting farm subsidies and raising taxes on the rich.

Republicans were still working on the details of their doomed bill Monday. One option would be to give the Pentagon more flexibility in determining the impact of the cuts. But some in the party oppose that idea.

“I didn’t spend all of those hours and two weeks on the floor of the Senate on the defense authorization bill to say, ‘Hey, do whatever you want,’ ” said Sen. John McCain (R-Ariz.). “I will adamantly oppose just giving it over to the executive branch. I took an oath to defend the Constitution.”

Senate leaders were still working Monday on how and when the bills will be brought up to fail. It will definitely happen by Thursday, they said.

Rosalind S. Helderman, Sean Sullivan, Ed O’Keefe, Zachary A. Goldfarb, Lisa Rein, Brady Dennis and Lori Aratani contributed to this report.