Former Sen. Alan Simpson (R-Wyo.) predicted Sunday that tax rates for the wealthy will likely go up next year.

Speaking on CBS’s “Face the Nation,” Simpson, a co-chairman of the Simpson-Bowles deficit commission, said he and Erskine Bowles, a former Clinton White House chief of staff and the panel’s other co-chairman, believe taxes will go up for the rich.

“I think Erskine and I both agree that if anybody out there who is, quote, rich doesn’t think their taxes go up, the drinks are on me, I’ll cover it,” Simpson said.

Bowles, however, noted that raising taxes on the wealthy wouldn’t be enough to bring down the nation’s deficit.

“Even if you raise the top rates back to the Clinton rates, that only creates $400 billion over 10 years. That’s $40 billion a year. We got a trillion-dollar-a-year deficit. That alone won’t solve the problem,” Bowles said.

Bowles said spending cuts must be made in order to bring down the debt.

“We have to slow the rate of growth of healthcare to the rate of growth of the economy,” Bowles said.

The deficit hawks are both worried over the impact from going over the “fiscal cliff” — a set of massive tax increases and budget cuts that will go into effect early next year unless Congress acts. Bowles said going over the cliff entails possible layoffs, estimating 2 million people could lose their jobs and the unemployment rate could climb to 9 percent.

“I think this would be a disaster to go over the cliff,” Bowles said.

Simpson lambasted lawmakers in both parties who argue going over the fiscal cliff would be politically advantageous for their respective parties.

“There’s something terribly bizarre and juvenile about that. To think your party comes ahead of your country, I don’t go for that at all,” Simpson said.

Bowles remains optimistic about a deal getting done, however.

“I’m a little more encouraged than if you would have asked me about it a week ago,” Bowles said. “They have started to tango now and any time you got two guys in there tangoing, you got a chance to get it done.”