Congressional Republicans have put all their focus in the looming fiscal battles into defunding health care reform, to the chagrin of deficit hawks who want to use the budget fight to push their own economic agenda.

Just days before the House Republican leadership caved in to the right wing of their party and decided to proceed with a strategy of demanding that a bill to fund the government after the end of the month also defund the health care reform law, a group of CEOs traveled to Washington with a very different message: Don’t mix Obamacare and the budget.

On Tuesday, a number of executives with the Campaign to Fix the Debt, an influential (and moneyed, raising $60 million at the end of last year, according to a report critical of the initiative) group of business leaders and politicians who lobby for debt reduction measures, met with senators and White House officials to discuss the upcoming fights to fund the government and raise the debt limit. According to one CEO who attended the meetings, the message from Fix the Debt was that Congress shouldn't link defunding the Obamacare battle with the fiscal fights.

“The budget should be discussed alone, it shouldn’t be something that comes with a certain other bill attached, like health care reform,” said Dominik Knoll, the CEO of the World Trade Center of New Orleans, a trade group bringing international business opportunities to Louisiana. He said there was consensus among the lawmakers they met with that the budget and health care should be kept separate. 

The group’s presence on Capitol Hill this week signals that it views the current stalemate over the budget and debt ceiling as an opening to push its fiscal agenda, which includes tax and entitlement reforms and, most importantly, an austerity plan to bring down the debt. Bringing health care into the mix distracts from any sort of deal that could be struck to cut spending or bring about reforms.

Earlier this week, Knoll, a member of Fix the Debt’s Louisiana chapter, was part of a contingent of business executives who attended a series of Washington meetings, including World Fuel Services Corporation (NYSE:INT) Chairman Paul Stebbins; Gregg Sherrill, chairman and CEO of Tenneco (NYSE:TEN); Dave Cote, chairman and CEO of Honeywell International (NYSE:HON), WhippleWood CPAs CEO Rick Whipple; and the head of the campaign, Maya MacGuineas.

Knoll said the group, which included a few others as well, met with Sens. Saxby Chambliss, R-Ga.; Mike Johanns, R-Neb.; Dan Coats, R-Ind.; Patty Murray, D-Wash.; Kelly Ayotte, R-N.H.; and Johnny Isakson, R-Ga. The group was also received at the White House, where it met with Valerie Jarrett, a senior adviser to the president, and Sylvia Matthews Burwell, who heads the Office of Management and Budget.

Knoll said he came away with a positive feeling that the parties he had met with knew they had to compromise to get through the budget and debt limit fights. Even the Republican senators they met with, Knoll said, seemed to understand that combining the spending bill, called a continuing resolution, with the Obamacare fight would be counterproductive.

It’s assumed that President Barack Obama won't acquiesce to defunding his own flagship health care legislation, meaning that pursuing a continuing resolution that defunds the law only brings the government a step closer to a shutdown. So why didn’t Fix the Debt bring this message to the people pushing this risky strategy, someone like Texas Republican Sen. Ted Cruz?

“I personally have not. I know there are talks, but it’s not something on my table, so I couldn’t really say too much to it,” Knoll said.

Though avoiding specifics, Knoll said the current fights are a good time to introduce measures to bring down the deficit. On the subject of sequestration cuts, Knoll said they should only be rolled back if replaced with equal or greater cuts.

“I feel that there is also opportunity right now with the budget, with the debt ceiling, with the continuing resolution, tax reforms, entitlements, those types of things, to really now structure it in a way that would not only put the deficit down but we would also be reducing the debt,” he said.

The message Knoll said he and his fellow executives brought to Washington was a widely shared concern about the fiscal crises looming in coming weeks. Uncertainty, the threat of either a government shutdown or worse, defaulting on the national debt, is keeping businesses from expanding, Knoll said. Lastly, Knoll and his corporate colleagues stressed that a deal at the 11th hour to avert crisis is still bad for the economy, because it still creates the uncertainty that causes businesses to hoard cash and consumers to lose confidence.

As the threat of a crisis looms, Democrats who want to avoid the Obamacare fight are already pointing out that even talking about defaulting on our debt is bad for the economy -- a lesson learned during the debt ceiling fight in 2011.

“As Congress struggled to raise the debt ceiling, the Dow Jones Industrial Average dropped more than 2,000 points, and Standard and Poor’s downgraded the U.S. credit rating,” Sen. Amy Klobuchar, D-Minn., said at a Joint Economic Committee hearing Wednesday on the economic costs of even threatening not to raise the debt ceiling.

Knoll, who heads a trade association that deals with companies both here and abroad, also stressed that political battles over government funding and paying the nation’s debts could hurt the economy. Foreign businesses don’t want to invest in selling or buying from the U.S. if it appears the government is struggling to keep itself running.

Though Knoll said the White House was receptive to the group's message, its militancy about the debt runs up against what Obama said on Wednesday when addressing the Business Roundtable, another group made up of corporate CEOs.

“Our deficits are coming down very fast,” the president said. “In fact, the IMF and other international organizations that had cautioned us previously about our deficits are actually now concerned that we're bringing our deficits down too fast. That's the assessment of the economists.”

As the 2013 budget year comes to a close at the end of the month, the Congressional Budget Office estimates the deficit will be $670 billion -- a major reduction from last year’s $1.09 trillion.

Knoll granted that Obama has done a “tremendous job” in reducing the deficit but said more can be done to tackle both the annual deficits and the national debt and now is “the time to act.”