“Let me put it very clearly,” says the five-term Republican senator from Kentucky. “I am not willing to raise taxes to turn off the sequester. Period.” On Jan. 1, Washington faces both a huge tax increase and an automatic spending cut known as the “sequester,” which could tip the economy back into recession. A newly emboldened President Obama is likely to take his soak-the-rich case straight to the people, I remind the senator. The political pressure to capitulate could become intense.

“Look, he may think it would be helpful to his presidency to continue to divide and demonize us,” says Mr. McConnell. “But my answer will still be short and firm: No. We won’t agree to any tax increases that will hurt the economy.”

This isn’t to say that next week, when the lame-duck congressional session begins to negotiate some kind of budget solution, taxes are off the table. Mr. McConnell is a realist. Republicans are willing to be “flexible” on raising revenues but, he hastens to add, only “in the context of broad-based, comprehensive tax reform.” He’s open to prying more out of the rich by closing tax loopholes. But he and his caucus of 45 Republicans want lower, not higher, rates.