House Speaker John A. Boehner and President Barack Obama met at the White House on Monday for another negotiating session on the fiscal cliff amid growing optimism that they can reach a deal to avoid the tax increases and automatic spending cuts due to take effect in a little more than two weeks.

It was the third face-to-face meeting between Boehner and Obama in the past eight days, and the first since word that Boehner had broken his stance against tax rate increases, offering to allow rates to rise on earnings over $1 million.

White House spokesman Jay Carney said in his daily briefing that “conversations continue” without elaborating on anything that was discussed at the 45-minute negotiating session late Monday morning. A Boehner spokesman also declined to offer any specifics.

“Everybody’s talking. So, that’s a good thing,” Majority Leader Harry Reid of Nevada said Monday.

Minority Leader Mitch McConnell of Kentucky declined to comment on Monday on the current status of talks or the latest offer by Boehner.

A former senior Obama aide that remains close to the administration said White House officials were hopeful of reaching an agreement. “There is optimism,” the former aide said. He said he believed a deal would need to be concluded on by Tuesday in order to be on the floor in either chamber before Christmas.

A senior House GOP aide said Obama and Boehner were already stretching the ability of staff to turn an agreement into a bill that could be reviewed by members and put to a vote before Christmas.

“It will probably be written down on three pages. But it will be 10 times the size of the Budget Control Act, which was 100 pages,” the aide said. He referred to the last debt deal (PL 112-25) that put in place automatic spending cuts starting in January.