WASHINGTON — With a scrappy unveiling of his formula to rein in the nation’s mounting debt, President Obama confirmed Monday that he had entered a new, more combative phase of his presidency, one likely to last until next year’s election as he battles for a second term.

Faced with falling poll numbers for his leadership and an anxious party base, Mr. Obama did not just propose but insisted that any long-term debt-reduction plan must not shave future Medicare benefits without also raising taxes on the wealthiest taxpayers and corporations.

He uncharacteristically backed up that stand with a veto threat, setting up a politically charged choice for anti-tax Republicans — protect the most affluent or compromise to attack deficits. Confident in the answers most voters would make, Mr. Obama plans to hammer on that choice through 2012, reflecting the fact that the White House has all but given up hopes of a “grand bargain” with Republicans to restore fiscal balance for years to come.

“I will not support — I will not support — any plan that puts all the burden for closing our deficit on ordinary Americans. And I will veto any bill that changes benefits for those who rely on Medicare but does not raise serious revenues by asking the wealthiest Americans or biggest corporations to pay their fair share,” Mr. Obama said. “We are not going to have a one-sided deal that hurts the folks who are most vulnerable.”