U.S. President Barack Obama is hailing a last-minute deal that avoids the so-called fiscal cliff but says it's just one step in a broader effort to boost the economy and shrink federal deficits. President Obama said in his radio and Internet address Saturday that the new law - approved by Congress on New Year's Day and signed 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, President Obama faces new battles in Congress over raising the country's $16.4 trillion borrowing limit, as well as more than $100 billion 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. President 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 federal debt ceiling. 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," President 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," President Obama said.