"Now that Congress has made the Bush-era tax cuts permanent for 98 percent of American workers, tax rate increases are off the menu. The president's only options for reducing the deficit are spending cuts, entitlement reform and tax reform."

On New Year's Day, Congress passed a bill that maintains current income tax rates for most people, but lets them increase on family income above $450,000. That compromise level is higher than the $250,000 threshold that Obama had proposed.

Cole argued that some combination of spending cuts, entitlement reform and tax reform have always been the only path to a balanced budget, but he said Obama and a "complicit media" have focused on taxes. However, he said that the non-expiring tax rates agreed to last week mean Obama has to look for other ways of raising revenue rather than rely on expiring rates.

"His administration will be forced to engage in an adult conversation about spending," he said.

Cole said that discussion will happen sooner rather than later, because that same bill pushed the spending sequester to March, which is also when the six-month stopgap spending resolution expires. In addition, the debt ceiling is about to be breached again.

"The budget deadlines approaching in the first three months of the new year provide the opportunity to achieve significant progress on spending reductions and entitlement reform," he said. "Let's hope the president has resolved to be a participant, not an obstacle."

While Cole and other Republicans have said the fiscal-cliff deal means the tax debate is over, Democrats have indicated they still want to explore additional tax revenue when the issue of tax reform comes up.