The White House says it remains “hopeful” that the fiscal cliff will be averted, despite comments from Senate Minority Leader Mitch McConnell, R-Ky., that the talks are at an “impasse.”

“We remain hopeful and optimistic that we can reach a deal,” White House Press Secretary Jay Carney told reporters at the White House. “We are engaging with Congress. … With a little give, we can get it done.”

But Carney poured cold water on the key Republican ask: that new revenue in any deal come from slicing tax breaks for the highest earners, not from higher rates. Rate increases and caps on deductions are both needed to reach a deficit reduction deal, Carney said.

President Barack Obama wants about $1.6 trillion in tax revenue from people making more than $250,000, as part of a $4 trillion deficit reduction package; some of that would come from higher rates, some from shrinking deductions. But that’s twice the sum that Obama and Speaker John A. Boehner, R-Ohio, discussed during their “grand bargain” talks in 2011.

The GOP, meanwhile, has complained that Obama hasn’t yet committed to serious entitlement changes even as they are being asked to give in on revenue.