WASHINGTON – Less than a month after averting one fiscal crisis, Washington began bracing Tuesday for another, as lawmakers in both parties predicted that deep, across-the-board spending cuts would probably hit the Pentagon and other federal agencies on March 1.

Party leaders say they see no clear path to compromise, particularly given a growing sentiment among Republicans to pocket the cuts and move on to larger battles over health and retirement spending.

Adding to the sense of inevitability is the belief that the cuts, known as the sequester, would improve the government’s bottom line without devastating the broader economy. Though the cuts would hamper economic growth, especially in the Washington region, the forecast is far less dire than with other recent fiscal deadlines.

Cuts to the military and the defense industry remain politically problematic. But Tuesday, even some of the Pentagon’s most fervent champions seemed resigned to the likelihood that the cuts would be permitted to kick in, at least temporarily.

“I think it’s more likely to happen. And I’m ashamed of the Congress, I’m ashamed of the president, and I’m ashamed of being in this body, quite frankly,” said Sen. Lindsey O. Graham, R-S.C.

“How do you go to somebody in the military who’s been deployed four or five times . . . and say, ‘For your good work over the last decade, we’re going to ruin the military; we’re going to make it harder for you to have the equipment you need to fight, and we’re going to reduce benefits to your family?’ ” he said.

Senate Armed Services Committee Chairman Carl Levin, D-Mich., was only slightly more optimistic, saying there is a an even-probability threat that the sequester will strike in March.

As the deadline approaches, legions of corporate executives, nonprofit officials, mayors and governors are working the phones and trekking to Capitol Hill in hopes of securing a last-minute deal. Cuts to government contracts have already triggered layoffs, particularly in the defense industry. And agency officials are warning of mass furloughs of government workers that could delay medical research, leave national parks understaffed and otherwise disrupt federal operations.

The sequester is a product of the 2011 fight over the national debt, when the new GOP House majority insisted on spending cuts equal in size to the increase in the federal debt limit. The result: Spending caps that would force President Barack Obama to slice $1 trillion from agency budgets over the next decade, along with $1.2 trillion in additional cuts that would hit automatically on Jan. 2, 2013, unless Congress agreed on a plan to replace them.

The sequester was designed to be abhorrent to both parties. With the exception of a few programs spared by Congress — including Medicaid, Medicare benefits and food stamps — every government account would be sliced by roughly the same amount. Many Republicans were queasy about a projected 9.4 percent reduction in military programs. And many Democrats were alarmed by the prospect of an 8.2 percent cut to Head Start, air-traffic-control operations and community development block grants.

Despite the threat, lawmakers riven by larger ideological differences over taxes and spending have not agreed on an alternative plan to generate $1.2 trillion in savings over the next decade. Late last month, in the throes of negotiations over the “fiscal cliff,” the White House and congressional leaders informed rank-and-file lawmakers that the sequester would kick in on Jan. 2.

That sparked a furious lobbying campaign by outgoing Defense Secretary Leon Panetta, who helped secure a deal to delay the sequester for two months.