WASHINGTON -- Still gridlocked over how or whether to avert the looming federal spending cuts known as sequestration, the two major parties found a new thing to argue about Wednesday: They don’t agree on when the budget cuts start going into effect.

Republicans said the spending cuts would start Friday. The White House said it was really Saturday.

Either way, the seemingly trivial dispute underscored the inability of the two sides to avert spending cuts neither side wanted when they were enacted and signed into law in 2011. President Barack Obama announced plans to meet Friday at the White House with congressional leaders of both parties, but neither side expected any action before the cuts start sometime Friday or Saturday. Indeed, Republicans in the House of Representatives signaled they’re already looking past the all-but-certain start of the spending cuts to the next budget fight, over the legislation needed to finance the entire government.

Apart from the cuts in spending to the current budget, the government runs out of money in March and will need an appropriation to stay open through the end of the fiscal year, on Sept. 30. House Republicans said Wednesday that they’d vote next week on a plan to finance the government, but would lock in the $85 billion in spending cuts taking effect soon. That move, certain to be rejected by Democrats, is likely to be part of the White House session Friday.

Obama did talk briefly about the budget impasse Wednesday with House Speaker John Boehner, R-Ohio, House Minority Leader Nancy Pelosi, D-Calif., Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky., when he joined them for the dedication of civil rights icon Rosa Parks’ statue inside the Capitol.

White House spokesman Jay Carney said the president hoped that the lawmakers would have a "constructive discussion” at their full meeting Friday, but the political sniping suggested otherwise.

"Compromise here in Washington can usually be measured by a willingness of one leader to put forward proposals that demonstrate tough choices by his side or her side," Carney said. "What we have not seen from the Republicans is anything like the willingness to compromise inherent in the proposals that the president has put forward."

McConnell complained that “the Democrats who control Washington still haven’t put forward a serious bipartisan plan; not the president and not his allies in Congress.”

“Now, less than 48 hours before the clock runs out, all they’ve offered is a gimmicky tax hike that’s designed to fail,” McConnell added. “I hope they’re not expecting a round of applause for this particular act of political bravery.”

New York Mayor Michael Bloomberg, who visited the White House on Wednesday, said the sequester mess was a pox on both the White House and Capitol Hill.

“Keep in mind sequestering was an idea that came out of 1600 Pennsylvania Avenue and the Senate and House, both sides of the aisle,” said Bloomberg, a Republican-turned-political independent. “This was something all of these elected officials find a good idea, and I find it fascinating that they are trying to blame each other for it. They all voted for it.”

As a prelude to Friday’s meeting, the White House and Democrats continued to outline the dire consequences that some Americans might find themselves in under sequester. Wednesday was Education Secretary Arne Duncan’s turn.