President Obama said Saturday that he's willing to compromise with Republicans on taxes and spending cuts in coming months, but will not budge on honoring America's obligations as the national debt this week topped $16.4 trillion – the congressionally set "debt ceiling."

"I will not compromise over ... whether or not Congress should pay the tab for a bill they’ve already racked up," Mr. Obama said in his taped weekly address, his first of the new year. "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. The last time Congress threatened this course of action, our entire economy suffered for it. Our families and our businesses cannot afford that dangerous game again."

Obama was referring to the 2011 debt-ceiling fight, which was resolved only by creating a set of mandatory spending cuts that were to take effect on Jan. 1, 2013, if Congress could not iron out its partisan differences about how to proceed. Those mandatory spending cuts were part of the “fiscal cliff,” which also included the expiration of Bush-era tax cuts.

The fiscal cliff debate went past the 11th hour before the House approved Senate legislation that allows taxes to be raised on Americans making more than $400,000 a year, while delaying by two months decisions over how to deal with $100 billion in automatic spending cuts.

House Speaker John Boehner was able to both override opposition to the plan from antitax Republicans and, though roughed up, win reelection as speaker. But he's made it clear that he will demand a dollar-to-dollar match between spending cuts and more borrowing.

With America's current debt at $16.4 trillion, Obama will shortly ask Congress to raise the ceiling to meet the country's obligations. Citing the fallout from the last debt-ceiling standoff, he warned Republicans to reconsider another fight.

“Our economy can’t afford more protracted showdowns or manufactured crises,” Obama said in his weekly address, adding that “the messy brinksmanship in Congress made business owners more uncertain and consumers less confident.”

In the Republican weekly address, Rep. Dave Camp of Michigan countered, "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," Representative Camp said.

The positions being taken don’t bode well for a chummy negotiation process. "If the Republicans hold their ground and the president holds his ground, the fight we just had over that fiscal cliff is going to look like child’s play compared to this battle," Time columnist Mark Halperin told Lester Holt on NBC’s “Today” show Saturday.

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The Wall Street Journal's Kimberley Strassel describes the fiscal cliff tax-hike deal as "Round One," in which the GOP took a beating on poor messaging, internal feuding, and a misread of Obama's tactics. "Round Two," she writes, will find the GOP looking for new openings to force the president to confront the spending side of the rising national debt.

"Republicans are convinced they can win this one," she writes. "Their thinking? The president can't use the threat of higher middle-class taxes to force the GOP to yield. Without the middle class as a hostage in the negotiations, they believe, the debt-ceiling debate will be entirely on spending and Mr. Obama's failure to confront the nation's $16 trillion debt."