Pablo Martinez Monsivais, Associated Press
White House Press Secretary Jay Carney gestures during his daily news briefing at the White House in Washington, Monday, June, 27, 2011.

WASHINGTON — President Barack Obama and the congressional Republican leadership are negotiating a debt deal privately. Publicly, they are digging in their heels.

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Obama and Vice President Joe Biden spent more than an hour with Senate Republican leader Mitch McConnell in the Oval Office on Monday, a rare private meeting among the three. Afterward, a McConnell aide said the three will continue to talk.

No new meetings were announced. But with the government's borrowing authority at stake, pressure was building to keep the financial markets at bay.

Obama and Democrats insist a deal must include some tax increases on the wealthy or on corporations. But before McConnell even walked into the White House, he had flatly rejected tax increases.

Still, White House spokesman Jay Carney said a "significant" deal was still likely.