During an exclusive interview with cnbc's John Harwood, President Obama says he's bent over backwards to work with Republians, but that he's exasperated, because "this is entirely unnecessary."

President Barack Obama said Wednesday that he is “exasperated” by the government shutdown but won’t negotiate with the Republicans until they pass an extension of funding to reopen it.

“Am I exasperated?” Obama said in an exclusive interview with CNBC three hours before he was set to meet with congressional leaders from both parties at the White House. “Absolutely, I’m exasperated because this is entirely unnecessary.

“I am exasperated with the idea that unless I say to 20 million people you can’t have health insurance, these folks will not reopen the government,” Obama added. “That is irresponsible.”

He said that if House Speaker John Boehner put a bill on the floor to reopen the government at current funding levels while long-term budget talks go on, it would pass.

“The only thing that’s stopping it right now is that John Boehner has not been willing to say no to a faction of the Republican Party that are willing to burn the house down because of an obsession with my health-care initiative,” he said.

He said it was “not acceptable for one faction of one party in one chamber” to shut down the government or risk an unprecedented default on the national debt because it wants the Affordable Care Act repealed.

“The message I have for the leaders is very simply: As soon as we get a clean piece of legislation that reopens the government -- and there is a majority for that now in the House of Representatives -- until we get that done, until we make sure that Congress allows Treasury to pay for things that Congress itself already authorized, we are not going to engage in a series of negotiations,” Obama said.

“If we get in a habit where a few folks, an extremist wing of one party – whether it’s Democrat or Republican -- are allowed to extort concessions based on a threat of undermining the full, faith and credit of the United States, then any president who comes after me… will find themselves unable to govern effectively.

“And that is not something I’m going to allow to happen.”

President Obama tells cnbc's John Harwood that the instability provided by a potential short-term budget fix won't work.

Asked about Wall Street’s relatively calm reaction to the crisis in the nation’s capital, Obama said it was out of step with the reality of the situation.

“I think this time’s different,” he said of the current shutdown and impasse. “I think they should be concerned.”

The interview came after Obama’s meeting with the Financial Services Forum, a group of high-profile business leaders and heads of the major banks

He said he told them, “democracy’s messy” and added a caution.

“When you have a situation in which a faction is willing to potentially default on U.S. government obligations, then we are in trouble. And if they’re willing to do it now, they’ll be willing to do it later.”

The president said he wasn’t blocking discussions about Obamacare, which kicked into high gear this week with the opening of state exchanges where the uninsured should purchase insurance.

“If they want to give me specific suggestions around how we can improve delivery of health insurance to people who need it…I’m happy to talk to him about it,” Obama said. “But I’m not going to do it subject to the threat that somehow America defaults on its obligations.”