As House Speaker John Boehner left his office building after finishing his response to President Barack Obama's remarks about averting economic calamity, CBS News' Jill Jackson overhead him say, "I didn't sign up for going mano-a-mano with the President of the United States."

During his address to the nation Monday night, Obama warned that the Republicans' unyielding approach to the US debt crisis was a "dangerous game" and urged Americans to press for compromise.

Watch Obama's speech here

Obama delivered the warning in a rare primetime speech as Republicans and Democrats remained deadlocked over a deal to raise the US debt ceiling and agree on how to bring ballooning US deficits under control.

The president rejected a Republican proposal to temporarily lift the debt limit, arguing it would leave the underlying problem unresolved and lead to a repeat of the current crisis in six months.

"That is no way to run the greatest country on Earth. It is a dangerous game we've never played before, and we can't afford to play it now. Not when the jobs and livelihoods of so many families are at stake," he said.

But with a potential US default looming in eight days time, Obama appealed to Americans to "make your voice heard."

"If you want a balanced approach to reducing the deficit, let your member of Congress know. If you believe we can solve this problem through compromise, send that message," he said.

The top Republican in the US House of Representatives John Boehner said that the United States "cannot default on its debt obligations," amid tense negotiations on raising the debt ceiling.

Boehner warned, "The American people will not accept an increase in the debt without significant spending cuts and reform."

Obama, he said, "has often said we need a 'balanced' approach -- which in Washington means: we spend more, you pay more... those tax increases will destroy jobs."

This video is from ABC News, broadcast Monday, July 26, 2011.

With additional reporting by Raw Story