Congressional leaders took an optimistic tone from an afternoon meeting at the White House, and Senate Minority Leader Mitch McConnell said he was "hopeful" he and Majority Leader Harry Reid could hash out a deal on Saturday to avert the year-end fiscal cliff.

Reid, McConnell and House Speaker John Boehner's office all said that the consensus from the meeting was that the Senate needs to take the next steps in any deal.

Reid called the meeting "constructive" and said he "hopes it produces something constructive." He said the Senate would be out of session on Saturday so he and McConnell could hash out a deal.

President Barack Obama did not offer a "new" proposal in the meeting, contrary to McConnell's expectations.

Rather, Obama reiterated previous positions on income-tax rates and other components of the cliff.

He asked Congressional leaders at the meeting for a concrete counterproposal, which Reid and McConnell will try to do on Saturday. If no agreement is reached, he will ask for an up-or-down vote on his own plan in Congress.

At 3:10 p.m., Obama began his meeting at Reid, McConnell, Boehner, and House Minority Leader Nancy Pelosi. It ended at 4:15 p.m, the White House said.

The meeting came after a frantic day in fiscal-cliff negotiations on Thursday, during which reports of a new offer from President Obama to Senate Republicans was quickly shot down by the White House and Democratic aides.

Check the blog for a full recap of the day's events.