"We are not close to a deal," Corker said. "I've been trying for three weeks — standing on my head, doing cartwheels — to try to pivot to entitlement reform. This is not a deal here." (Read More: Boehner Proposing a "Plan B" Option )

A source familiar with the negotiations told CNBC the president's new proposal on Monday included lowering his revenue target again to $1.2 trillion, and moving up his threshold for tax hikes on the rich to households making over $400,000. Until now, Obama had insisted on raising taxes on those making $250,000 and above. Boehner said he's willing to go to a million dollars. (Read More: Obama Moves Goal Posts 'Out of the Ballpark,' says Lindsey )

Obama's new offer did detail some spending cuts and saving projections. But Corker characterized them as "nebulous," insisting that any deal needs to include a trillion dollars in entitlement reforms.