President Barack Obama is hailing a last-minute deal that avoids the so-called "fiscal cliff" but insists it is just one step in a broader effort to boost the economy and shrink federal deficits.

Mr Obama said in his radio and internet address today that the new law - approved by Congress on New Year's Day and signed on Thursday - raises taxes on the wealthiest Americans while preventing a middle-class tax hike that could have thrown the economy back into recession.

With the "fiscal cliff" crisis barely over, Mr Obama faces new battles in Congress over raising the country's 16.4 trillion dollars borrowing limit, as well as more than 100 billion dollars in automatic spending cuts for the military and domestic programs which were 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.

Mr Obama - speaking from Hawaii, where he is on holiday 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 federal debt ceiling without negotiations. The nation's credit rating was downgraded the last time lawmakers threatened inaction on the debt ceiling, in 2011.

"Our families and our businesses cannot afford that dangerous game again," Mr Obama said.

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," Mr 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.