Obama said in his radio and Internet address Saturday that the fiscal cliff deal, approved by Congress on New Year’s Day and signed Thursday, raises taxes on the wealthiest Americans while preventing a middle-class tax increase that could have thrown the economy back into recession.

With one crisis behind him, Obama faces new battles in Congress over raising the country’s $16.4 trillion borrowing limit, as well as scaling back more than $100 billion in automatic spending cuts for the military and domestic programs. The cuts are delayed by two months under the compromise.

Lawmakers promise to replace those across-the-board cuts with more targeted steps that could take longer to implement.

Obama, speaking from Hawaii, where he is on vacation with his family, said he is willing to consider more spending cuts and tax increases to reduce the deficit.

But he said he will not compromise over his insistence that Congress lift the debt ceiling. The nation’s credit rating was downgraded the last time lawmakers threatened inaction on the debt ceiling, in 2011.

“If Congress refuses to give the United States the ability to pay its bills on time, the consequences for the entire global economy could be catastrophic,” Obama said. “Our families and our businesses cannot afford that dangerous game again.”

If elected officials from both parties “focus on the interests of our country above the interests of party, I’m convinced we can cut spending and raise revenue in a manner that reduces our deficit and protects the middle class,” Obama said.

In the Republican address, Rep. Dave Camp of Michigan said that as attention again turns to the debt limit, “we must identify responsible ways to tackle Washington’s wasteful spending.”

Americans know that “when you have no more money in your account and your credit cards are maxed out, then the spending must stop,” Camp said.

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By Matthew Daly