Correction: An earlier version of this article incorrectly said that potential budget cuts would cost hospitals belonging to the American Hospital Association an estimated $50 billion a year in Medicare payments. The association estimates that its members would lose $45 billion over nine years without a revised deficit agreement. This version has been corrected.

Health-care and defense lobbyists are quickly gearing up for a major lobbying and public relations campaign in response to this week’s debt-limit deal, which could force hundreds of billions of dollars in cuts for two of Washington’s most powerful industries.

The compromise bill that averted a government default this week includes $1.2 trillion in mandatory cuts over the next decade if Congress can’t agree on a broader deficit reduction plan by December. Most of that amount targets the Pentagon and Medicare providers.

The arrangement has set off alarms among major defense contractors, hospital firms and others that would stand to lose billions if Congress doesn’t decide on a different plan. The first focus of the nascent lobbying campaign will be a bipartisan “supercommittee”to be named later this month that will attempt to hash out a compromise, according to lobbyists, trade groups and others involved in the effort.

The message from both industries will be similar: Any massive reductions will hurt national priorities and undermine job growth.

“It will be a full-court press to work with the committee to make our views known,” said Richard Pollack, executive vice president of the American Hospital Association, whose members would lose an estimated $45 billion over nine years in Medicare payments under the trigger scenario. “Our hospitals are in every congressional district in the country. Our patients are Republicans and Democrats. We are very concerned about where this is going to go.”

The architecture of the debt deal is aimed in part at forcing compromise by threatening two of Washington’s political sacred cows: Medicare for Democrats and defense spending for Republicans. The idea is that, faced with the possibility of draconian cuts, lawmakers will be swayed to find savings and revenue elsewhere to close the long-term budget gap.

The approach appears tailor-made to produce a frenzy on K Street, where major lobbying firms and trade groups are already laying out strategies for protecting their interests.

“It’s going to be pain versus pain for a lot of people,” said veteran lobbyist Tony Podesta of the Podesta Group, whose clients include major defense contractors and health-care firms. “There’s going to be a focus on the 12 and a focus on the leadership and a focus on the administration. Decisions will get made by a smaller number of people than you learned about in high school.”

The health-care industry is one of the most powerful lobbies in Washington, spending nearly $300 million to influence Congress and the administration in the first half of 2011, according to lobbying data from the Center for Responsive Politics. The hospital sector alone — which is particularly upset over the proposal to slash provider payments — has given nearly $50 million in campaign contributions to federal candidates since the 2008 election, records show.

On the defense side, Lockheed Martin, Boeing and other major contractors and trade groups have spent nearly $70 million on lobbying this year. The sector has also given about $50 million to candidates since 2008, according to the Center for Responsive Politics.

The deficit deal includes about $350 billion in guaranteed cuts for the Pentagon and other defense-related programs, plus up to $600 billion in additional reductions that will be triggered if Congress fails to reach a different agreement.

Marion C. Blakey, president of the Aerospace Industries Association, said in a statement this week that the deal “dangles a Sword of Damocles over our national security” if a compromise is not reached.

“The $600 billion in additional cuts to defense that are part of the so-called ‘trigger’ deal are a dangerous approach that could compromise our national security for decades to come,” Blakey said. “. . . National security funding should not be treated as a piggy bank for deficit reduction, while the real drivers of our fiscal problems, such as entitlement spending, are off the table.”

Ellen Miller, executive director of the Sunlight Foundation, which tracks money in politics, predicted that the deficit-reduction talks will produce a “lobbying-palooza” on Capitol Hill.

“Any bill that involves this kind of money, the companies with a vested interest are going to spend whatever it takes to protect their bottom lines,” she said.