WASHINGTON — The White House and Republicans kept up the unrelenting mudslinging Sunday over who’s to blame for roundly condemned budget cuts set to take effect at week’s end, with the administration detailing the potential fallout in each state and governors worrying about the mess.

But as leaders rushed past each other to decry the potentially devastating and seemingly inevitable cuts, they also criticized their counterparts for their roles in introducing, implementing and obstructing the $85 billion budget mechanism that could affect everything from commercial flights to classrooms to meat inspections. The GOP’s leading line of criticism hinged on blaming President Barack Obama’s aides for introducing the budget trigger in the first place, while the administration’s allies were determined to illustrate the consequences of the cuts as the product of Republican stubbornness.

Former Republican National Committee chairman Haley Barbour, aware the political outcome may be predicated on who is to blame, half-jokingly said Sunday, “Well, if it was a bad idea, it was the president’s idea.”

Sen. Claire McCaskill, D-Mo., said there was little hope to dodge the cuts “unless the Republicans are willing to compromise and do a balanced approach.”

No so fast, Republicans interjected.

“I think the American people are tired of the blame game,” said Sen. Kelly Ayotte, R-N.H.

Yet just a moment before, she was blaming Obama for putting the country on the brink of massive spending cuts that were initially designed to be so unacceptable that Congress would strike a grand bargain to avoid them.

Obama nodded to the squabble during his weekly radio and Internet address.

“Unfortunately, it appears that Republicans in Congress have decided that instead of compromising — instead of asking anything of the wealthiest Americans — they would rather let these cuts fall squarely on the middle class,” Obama said Saturday, in his last weekly address before the deadline.

“We just need Republicans in Washington to come around,” Obama added. “Because we need their help to finish the job of reducing our deficit in a smart way that doesn’t hurt our economy or our people.”

With Friday’s deadline nearing, few in the nation’s capital were optimistic that a realistic alternative could be found and all sought to cast the political process itself as the culprit. If Congress does not step in, a top-to-bottom series of cuts will be spread across domestic and defense agencies in a way that would fundamentally change how government serves its people.

Obama senior adviser Dan Pfeiffer told reporters the GOP is “so focused on not giving the president another win” that they will cost thousands of jobs. To back up their point, the White House released state-by-state tallies for how many dollars and jobs the budget cuts would mean to each state.

“The Republicans are making a policy choice that these cuts are better than eliminating loopholes,” Pfeiffer said.

And, yes, those cuts will hurt. They would slash from domestic and defense spending alike, leading to furloughs for hundreds of thousands of government workers and contractors.

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.

In Virginia, for instance, 90,000 Defense Department civilian employees could be furloughed, including nurses at Army hospitals, said Sen. Tim Kaine, D-Va. He also said ship-repair contractors could lay off 300 of their 450 employees.

“There is no reason that this has to happen. We just need to find a balanced approach,” Kaine said.

White House officials also pointed to Ohio as another state that would be hit hard: $25.1 million in education spending and another $22 million for students with disabilities. Some 2,500 children from low-income families would also be removed from Head Start programs.

Officials said their analysis showed Kentucky would lose $93,000 in federal funding for a domestic abuse program, meaning 400 fewer victims being served in Senate Minority Leader Mitch McConnell’s home state. Georgia, meanwhile, would face a $286,000 budget cut to its children’s health programs, meaning almost 4,200 fewer children would receive vaccinations against measles and whooping cough.

White House officials said Nevada would face military furloughs totaling $12.1 million in reduced pay, a $424,000 cut to pay for meals for seniors and an almost $2 million reduction for clean air and water programs.

The White House compiled the state-by-state reports from federal agencies and its own budget office. The numbers reflect the impact of the cuts this year. Unless Congress acts by Friday, $85 billion in cuts are set to take effect from March to September.

As to whether states could move money around to cover shortfalls, the White House said that depends on state budget structures and the specific programs. The White House did not have a list of which states or programs might have flexibility.

Republican leaders were not impressed by the reports for the 50 states and the District of Columbia.

“The White House needs to spend less time explaining to the press how bad the sequester will be and more time actually working to stop it,” said Michael Steel, a spokesman for House Speaker John Boehner of Ohio.

Some governors said the impasse was just the latest crisis in Washington that is keeping businesses from hiring and undermining the ability of state leaders to develop their own spending plans.

“It’s senseless and it doesn’t need to happen,” said Gov. Martin O’Malley, D-Md., during the annual meeting of the National Governors Association over the weekend.

“And it’s a damn shame, because we’ve actually had the fastest rate of jobs recovery of any state in our region. And this really threatens to hurt a lot of families in our state and kind of flat-line our job growth for the next several months,” O’Malley said.

Obama did not mention the budget cuts in remarks before his dinner with the governors Sunday evening at the White House; he is expected to address the issue in a speech Monday morning to the same group. But time is running out and hope is waning.

Connecticut Gov. Dan Malloy said it is past time for both sides to sit down to help dodge cuts that will hurt all states’ budgets.

“Come to the table, everyone. Everybody. Let’s work this thing out. Let’s be adults,” said Malloy, a Democrat.

Sen. John McCain, R-Ariz., called the defense cuts “unconscionable” and urged Obama to call lawmakers to the White House or the presidential retreat of Camp David for a last-minute budget summit.

“I won’t put all the blame all on the president of the United States. But the president leads. The president should be calling us over somewhere — Camp David, the White House, somewhere — and us sitting down and trying to avert these cuts,” McCain said.

LaHood, who served as a Republican representing Illinois in the U.S. House, urged his colleagues to watch Steven Spielberg’s film about President Abraham Lincoln’s political skills.

“Everybody around here ought to go take a look at the ‘Lincoln’ movie, where they did very hard things by working together, talking together and compromising,” said LaHood. “That’s what’s needed here.”

LaHood and Duncan were the only representatives from the administration to appear on Sunday shows. The White House did not book any of its senior aides.

Barbour, Malloy and McCain appeared on CNN’s “State of the Union.” McCaskill was interviewed on “Fox News Sunday.” Ayotte, Duncan and Kaine spoke with CBS’ “Face the Nation.” LaHood appeared on both CNN and NBC.