Such an effort would thrust Washington's traditionally cautious and pragmatic business lobby into open warfare with the Tea Party faction, which has grown in influence since the 2010 election and won a series of skirmishes with the Republican establishment in the last two years.  "We are looking at ways to counter the rise of an ideological brand of conservatism that, for lack of a better word, is more anti-establishment than it has been in the past," said David French, the top lobbyist at the National Retail Federation. "We have come to the conclusion that sitting on the sidelines is not good enough."  (Read more: Obama seeks opening with GOP leader)  Some warned that a default could spur a shift in the relationship between the corporate world and the Republican Pary. Long intertwined by mutual self-interest on deregulation and lower taxes, the business lobby and Republicans are diverging not only over the fiscal crisis, but on other major issues like immigration reform, which was favored by business groups and party leaders but stymied in the House by many of the same lawmakers now leading the debt fight.  Joe Echevarria, the chief executive of Deloitte, the accounting and consulting firm, said, "I'm a Republican by definition and by registration, but the party seems to have split into two factions."  While both parties have extreme elements, he suggested, only in the G.O.P. did the extreme element exercise real power. "The extreme right has 90 seats in the House," Mr. Echevarria said. "Occupy Wall Street has no seats."  (Read more: Stocks seem to be signaling a debt deal)  Moreover, business leaders and trade groups said, the tools that have served them in the past — campaign contributions, large memberships across the country, a multibillion-dollar lobbying apparatus — do not seem to be working.  "There clearly are people in the Republican Party at the moment for whom the business community and the interests of the business community — the jobs and members they represent — don't seem to be their top priority," said Dan Danner, the head of the National Federation of Independent Businesses, which spearheaded opposition to President Obama's health care law among small businesses."They don't really care what the N.F.I.B. thinks, and don't care what the Chamber thinks, and probably don't care what the Business Roundtable thinks."  The lawmakers seem to agree. Representative Randy Neugebauer, Republican of Texas and a Tea Party caucus member, said in an interview on Wednesday that if American corporations wanted to send their money elsewhere, that was their choice.  "We have got to quit worrying about the next election, and start worrying about the country," said Mr. Neugebauer, who sits on the House Financial Services Committee and is a recipient of significant donations from Wall Street.  Few of the most conservative House lawmakers draw substantial support from business political action committees, and business lobbyists acknowledged that the mere suggestion they were considering backing primary challenges next year could enhance grass-roots support for the very lawmakers they want to defeat. But the dysfunction in Washington has now turned so extreme, they said, that they had few other options.  (Watch: Does Obama want to break the GOP?)  "What we want is a conservative business person, but someone who in many respects will be more realistic, in our opinion," said Bruce Josten, the top lobbyist at the U.S. Chamber of Commerce, the single biggest lobbying organization in Washington.  In the two previous battles over the debt limit many chief executives were reluctant to take sides, banding together in groups like Fix the Debt, which spent millions of dollars on a campaign urging Democrats and Republicans to work toward a "grand bargain" on the budget. But with shutdown a reality, and the clock ticking toward default,some of those same executives now place the blame squarely on conservative Republicans in the House.  "It's clearly this faction within the Republican Party that's causing the issue right now," said David M. Cote, the chief executive of Honeywell and a steering board member of Fix the Debt.  The rift, these industry executives acknowledge, reflects longstanding tensions that sometimes emerge between the agendas of corporate executives and those embraced by the conservative wing of the Republican Party.  "We ask them to carry our water all the time," said one corporate sector lobbyist, who demanded anonymity in order to speak frankly about the relationship with Republicans. "But we don't necessarily support them 100 percent of the time.And what has happened is the rise of an ideological wing that is now willing to stand up to business interests."  Despite their diminished leverage, business leaders said they would step up their appeals for an agreement.  (Read more: Europe stocks higher on US budget progress)  Most of the officials said they agree in principle with conservative lawmakers about the need to cut federal spending or roll back parts of Obamacare, but said using the threat of shutdown — or worse, of a debt default — to extract those concessions was both ineffective and dangerous.  Mr.Josten said he had been on Capitol Hill every day this week counseling compromise.  "The name calling, blame gaming — using slurs like jihadist, terrorist, cowards, that kind of language — it does not get you to a deal," Mr. Josten said of the advice he is giving to Democrats and Republicans. "The problem is everybody is in the same corner here and everybody has to try to save some face."  To some extent, the Chamber itself, along with other lobbying groups, helped create the conditions for Washington's impasse.  (Read more:Boehner to ask House for short-term debt deal)
With the federal government pushing toward a budget default, big business groups are worried they have lost sway over the GOP majority in the House.