Fiscal Cliff

Under current law, the 35 percent top tax rate is scheduled to expire on Jan. 1, and would automatically go to 39.6 percent. Boehner's proposal would allow that rate to rise as scheduled at a threshold of $1 million — putting it back to where it was during the Clinton administration. 

The White House has not accepted the proposal and the source could not confirm any additional talks were held on Sunday between Obama and Boehner.

With just over two weeks before the fiscal cliff's $600 billion in automatic tax hikes and spending cuts are triggered, threatening a new recession, there is little time to craft a comprehensive deal that will satisfy both Democrats and Republicans.

Until the latest Republican offer, made on Friday, Boehner had insisted on extending all of the Bush era's lower tax rates, resisting Obama's demand to let the marginal rates rise on income above $250,000. A rising chorus of business executives also had urged Republicans to agree to this.

Some lawmakers and congressional aides had predicted that Republicans, once serious negotiations began, might try to raise the $250,000 threshold, say to $500,000 or $1 million. They also speculated that Republicans, if forced into a tax rate hike on the upper-income groups, might seek a smaller increase, say to around 37 percent.