In his weekly radio and Internet address, the president said the U.S. economy is gaining traction five years after a financial sector crisis spread to the larger economy and "the last thing we need is for Washington to manufacture another" crisis.
"But that's what will happen in the next few weeks if Congress doesn't meet two deadlines," he said.
Obama said the federal government will shut down Oct. 1 unless Congress passes a budget by Oct. 1, and the government will run out of money to pay its bill if Congress does not authorize an increase in the federal borrowing limit.
"Now, Democrats and some reasonable Republicans are willing to raise the debt ceiling and pass a sensible budget -- one that cuts spending on what we don't need so we can invest in what we do," the president said.
"But there's also a faction on the far right of the Republican Party who've convinced their leadership to threaten a government shutdown if they can't shut off the Affordable Care Act," he said. "Some are actually willing to plunge America into default if they can't defund the Affordable Care Act.
"Think about that," Obama said. "They'd actually plunge this country back into recession -- all to deny the basic security of health care to millions of Americans."
However, the president said, "that's not happening. And they know it's not happening."
"The United States of America is not a deadbeat nation," he said. "We are a compassionate nation. We are the world's bedrock investment. And doing anything to threaten that is the height of irresponsibility. That's why I will not negotiate over the full faith and credit of the United States. I will not allow anyone to harm this country's reputation, or threaten to inflict economic pain on millions of our own people, just to make an ideological point."
Obama said Congress could fix the problem "tomorrow."
"Then we can declare an end to governing by crisis and govern responsibly, by putting our focus back where it should always be -- on creating new jobs, growing our economy, and expanding opportunity not just for ourselves, but for future generations."