The Obama administration is asking to eliminate Congress’ role in raising the debt ceiling as part of a fiscal cliff deal, Senate Minority Leader Mitch McConnell, R-Ky., told Roll Call in an interview Thursday.

The White House dispatched Treasury Secretary Timothy F. Geithner to Capitol Hill earlier in the day, and his meeting with McConnell clearly did not go well from the Republican leader’s perspective. In a public statement released after the meeting, McConnell said talks “took a step backward.” When asked what that meant, McConnell mentioned the debt ceiling issue specifically.

“I think it was a meeting just to show that there was a meeting,” McConnell said. He said negotiations are in worse shape than they were two weeks ago, when leaders huddled at the White House. “I don’t think they were asking for $1.6 trillion in new revenue [two weeks ago] and they also want a permanent debt ceiling increase,” he said.

McConnell said that both issues constituted “highly irresponsible talk” and said the White House efforts Thursday were not what he “would consider … serious.”

Geithner told Bloomberg TV recently that the U.S. should eliminate the debt ceiling “the sooner the better.”

One source familiar with the conversation said the White House would like a new law written that would take away the authority of Congress to approve the extension of the nation’s borrowing capacity and leave it solely in the hands of the president. The votes to raise the debt ceiling would be eliminated entirely and automatic increases would be triggered, said two additional Hill sources.

A senior administration official contested that the $1.6 trillion figure is higher than the target set previously by the White House, pointing to a September 2011 budget blueprint submitted to Congress by President Barack Obama that included $1.5 trillion target for tax reform. The official did not immediately respond to a question about the debt ceiling request.

A House GOP leadership aide confirmed that Geithner asked for the same “permanent” extension of the debt ceiling from Speaker John A. Boehner, R-Ohio, and House Majority Leader Eric Cantor, R-Va. in their meeting Thursday.

Top Democrats, from Obama to Senate Majority Leader Harry Reid, D-Nev., have been saying all week that an increase in the debt limit would have to be part of any package. Other Democrats, such as House Minority Leader Nancy Pelosi of California, have suggested that the 14th Amendment could be invoked to remove Congress from the equation.

“The validity of the public debt of the United States, authorized by law, including debts incurred for payments of pensions and bounties for services in suppressing insurrection or rebellion,” a key sentence in the amendment born out of the Civil War reads, “shall not be questioned.”

White House spokesman Jay Carney sidestepped a question Thursday about whether the White House was looking for an agreement to raise the debt ceiling as part of fiscal cliff negotiations.

“In whatever manner it comes, it should be done soon and without drama,” Carney said at his daily briefing. “But we cannot have the kind of situation where there was harm done even with the threat of default. There was significant damage done to our economy, significant damage done to consumer confidence simply when the prospect of default was in the air in 2011, and we shouldn’t allow that to happen again.” But he said including it in any broad fiscal cliff agreement would be “entirely appropriate.”

Carney also responded to Boehner’s comments that any debt limit hike must be matched or exceeded by spending cuts.

“Asking that a political price be paid in order for Congress to do its job to ensure that the United States of America pays its bills and does not default for the first time in its history is deeply irresponsible. It was deeply irresponsible in the summer of 2011, and it would be deeply irresponsible if we were to see that kind of approach taken again,” Carney said.

According to a House leadership aide, Geithner’s offer also included an immediate increase in both top marginal rates as well as capital gains and dividends to bring in $960 billion; additional tax increases equal to $600 billion, returning to the 2009 level on the estate tax, and a multi-year stimulus package of at least $50 billion for fiscal year 2013 alone.

Republicans ripped the offer as nothing more than a reiteration of the president’s budget proposal from earlier this year, and they complained that it included no entitlement reforms.

“This offer represents a complete break from reality. There were only seven weeks between Election Day and Christmas. The White House has now completely wasted three of them. After weeks of negotiations, they just demanded all of their favorite proposals, with no sign of compromise whatsoever,” said one Congressional Republican aide familiar with the White House proposal.

Daniel Newhauser and Emily Pierce contributed to this report.