If President Barack Obama steps away from the Republican deficit-reduction proposal advanced Monday by House Speaker John Boehner, "we will go over the 'fiscal cliff,'" predicted Sen. Tom Coburn.

That said, the Oklahoma Republican added he doesn't want to see the negotiations continue to play out on the front pages or at campaign-style events.

"All this jockeying in public -- we need real leadership right now. There shouldn't be anything offered in public," Coburn said on CNN's "Erin Burnett OutFront." "What it should be is the president and Speaker Boehner in a room and nobody comes out of the room until this is solved."

"I'm okay to compromise even on some of my issues if in fact we'll solve the problem," he continued. "But what we have is a game being played ... for the extreme right wing and the extreme left wing in this country rather than coming together and leading and solving the problem."

Coburn was appointed by the top Senate Republican to Obama's 2010 bi-partisan deficit reduction panel chaired by Alan Simpson and Erskine Bowles. He was also a member of the informal group known as the "Gang of Six," which sought to write deficit reduction legislation.

Boehner's proposal was blasted by White House Communications Director Dan Pfeiffer for failing to "meet the test of balance," in particular on the issue of tax increases. On that sticking point, Republicans -- including Coburn -- favor increasing federal government revenues through elimination of tax code loopholes and limiting or capping deductions. Obama maintains that an increase in the tax rates paid by wealthy individuals must be part of a deal.

Some non-partisan analysts, including the Congressional Research Service, have said the increased revenues from handling deductions and loopholes alone would fall short of the targets.

"I've been studying this for seven years. That's baloney," Coburn replied. "It's easy to get $800 billion out of the wealthy in this country by limiting deductions and taking away options that are specifically benefit only the well off in this country."

He and other Republicans have described Boehner's proposal as similar to one Bowles, a Democrat, advanced in the fall of 2011. In addition to maintaining the Bush-era tax breaks on all income levels, it would accomplish $2.2 trillion in savings, among them $600 billion in non-entitlement spending cuts and $800 billion in "health savings."

Bowles said in a Monday statement that the "approach outlined in the letter Speaker Boehner sent to the President does not represent the Bowles-Simpson plan, nor is it the Bowles plan."

"I'm certain that if this is not good enough for the White House, we will go over the fiscal cliff," Coburn said, "because this is a compromise on taxes, this is a compromise on mandatory spending, and it's a compromise on discretionary spending over what the select committee had debated."