Congress is deadlocked over exactly what a debt-limit deal should look like. But for the country’s major business interests, the specifics of a deal aren’t what matter most right now— their most pressing need is to simply have an agreement to raise the limit.

Calling the possibility of default “unthinkable” and “unacceptable,” the U.S. Chamber of Commerce has been lobbying Congress to support Republican House Speaker John A. Boehner’s plan to reduce the nation’s debt, as have hundreds of smaller allied groups and the National Federation of Independent Business.

But when asked what was most important to the chamber at this stage of the debt talks, communications director Blair Latkoff responded: “The chamber’s priority is ensuring the debt ceiling is increased. The consequences would be great if we don’t act. Congress and the administration need to reach a deal to prevent the U.S. from defaulting on its financial obligations.”

I asked the NFIB whether the key difference between the proposals by Boehner (R-Ohio) and Senate Majority Leader Harry Reid (D-Nev.) – Boehner’s plan for a two-step approach that would combine a short-term extension with a later stage of triggered budget cuts – was critical to finalizing a deal.

“I’m not sure that would be problematic for us [if Congress and the White House accept the two-step deal], though I can see why the leadership in the House wants it in there…I’m not sure I feel strongly about it,” said Kevan Chapman, an NFIB spokesman. He added, “I think small businesses are just sick of what’s happening right now in Washington.”

Some business groups are turning their fire on the conservative, tea party-backed Republicans who refused to support Boehner’s plan on Thursday, forcing him to delay a vote on the measure.

“It’s a national and international crisis. Members of Congress in my view should stop playing around with theory and ideology and look at reality,” said Charlie Kolb, president of the Committee for Economic Development, a pro-business think tank with a membership of more than 200 corporate executives.

“Some of these holdouts have been pennywise and pound foolish, and I think it will hurt Republicans,” said Kolb, a former staffer in the Reagan and George H.W. Bush administrations. “Independents are breaking more with the Democrats, in terms of who’s taking a responsible approach. You can’t let ideological rigidity get in the way of a practical outcome.”