McConnell: GOP 'prepared to do a grand bargain' on budget

"We are prepared to do a grand bargain," McConnell told CBS News. "We have to have a willing president — you don't get these deals done without a president who is serious about getting an outcome."

The minority leader argued that the single biggest issue in Washington was the financial health of entitlement programs, warning that he viewed them as "unsustainable" in their current form.

"The biggest challenge we have for the future is the unsustainable path of our entitlements — very popular programs, the eligibility for which needs to be adjusted in order to meet the demographics of America," McConnell said. "Regret[tably], after six months of discussions the Speaker [John Boehner (R-Ohio)] and I had with the president, the president was unwilling to make this kind of eligibility change unless we gave him such a huge tax increase that [it] would have brought the economy to a halt."

Pressed by host Charlie Rose about reports that it was Boehner who walked away from the negotiating table, McConnell said he felt confident in the stance the Republican leadership took.

"I read the same articles. I thought the Republicans came out very well in Congress," McConnell said.

But the Kentucky lawmaker said he remains willing to re-enter negotiations, and to put some tax code reforms on the table — although he did not say explicitly whether he would consider legislation that would result in a net increase in taxes.

"I'm ready to sit down with this president or the next president and have the same discussion we had last year and reach a conclusion. I understand our friends on the other side live every day to raise taxes. I know that, I know that's important to them," McConnell said.

He also downplayed the notion that the president hadn't done enough to personally court congressional leaders through social invitations to White House functions.

"This is not a frivolous debate. This is not a personality conflict," McConnell said.