WASHINGTON (CNN) -- Now we're getting somewhere. Expected concessions by House Speaker John Boehner have moved negotiations on avoiding the fiscal cliff to a new level as the deadline for Congress to act shrinks to two weeks.
Sources told CNN over the weekend that Boehner's latest proposal dropped Republican opposition to two key demands by President Barack Obama -- higher tax rates on the wealthiest Americans and an automatic extension of the federal debt limit.
Boehner's office insisted no deal had been reached, but didn't dispute the information from the sources about the concessions.
"The lines of communication remain open but there is no agreement, nor is one imminent," said Boehner's spokesman, Michael Steel.
Congress had been scheduled to end its work last week, but legislators will return Monday with leaders warning members to be prepared to stay until Christmas and then return after the holiday until the year's end.
While the latest twists in the negotiations indicate a possible breakthrough, Boehner's offer also included hardline positions on spending cuts and reforming entitlement programs such as Social Security, Medicare and Medicaid that are opposed by Obama's liberal base.
The Ohio Republican's move sought to shift the onus on Obama to bring the Democratic position on spending cuts and entitlement reforms closer to the changes sought by the Boehner and the GOP.
Obama has repeatedly said that once Republicans accepted that tax rates on high-income Americans must increase, he would be willing to negotiate on other issues.
The president also has insisted that raising the federal debt ceiling should be separated from the political process of negotiating deficit reduction.
With the federal debt approaching the current ceiling of $16.4 trillion, Boehner's new offer would allow the government to again raise the borrowing cap -- a move that has faced strong GOP opposition since Republicans swept the U.S. House in 2010.
Boehner has consistently insisted that any increase in the debt limit must be offset by equal or greater spending cuts.
It was not immediately clear if his new proposal yielded on that demand, or whether Boehner will insist that proposed spending cuts in his plan must offset any debt limit increases.
According to one source, who spoke on condition of not being identified further, Boehner also proposed allowing tax rates on household incomes over $1 million to return to the higher rates of the 1990s while extending current reduced rates for all income up to that threshold.
In addition, his proposal includes a chained Consumer Price Index, which takes into account changes in quantity and prices of products, and an increase in the age of eligibility for Medicare, according to a source familiar with the talks.
Those two steps would affect benefits for senior citizens and other participants in entitlement programs, and labor unions and advocacy groups for the elderly were expected to oppose them.
A source familiar with the talks called Boehner's offer "insufficient on revenue and rates."
However, the White House does consider it "progress" and reiterated Steel's statement, saying that the "lines of communication are open," the source said.
Obama and Boehner did not speak Sunday, sources said.
The president demands that tax rates increase on incomes over $250,000, a stance that was central to his re-election campaign and is supported by most Americans, according to consistent poll results.
Boehner has been under pressure from the White House, Democrats, the business community and some fellow Republicans to give up a staunch opposition to any increase in tax rates.
A separate source said there was not enough time to get a deal passed before Christmas. If a deal gets reached soon, then passage by January 1 would be tight but achievable, the source said.
Last week, Democratic Rep. Chris Van Hollen said a deal would have to be reached by Christmas to allow enough time for the legislative process to approve the required measure or measures by the end of the year.
Boehner previously had offered to increase tax revenue by eliminating unspecified deductions and loopholes, but drew the line at allowing any rates to go higher.
Conservatives trying to shrink the federal government generally oppose increasing tax revenue. They are particularly opposed to higher tax rates because history shows that once rates go up, it is difficult to later reduce government revenue by lowering them again.
Obama and Democrats argue that increased revenue, including higher tax rates on the wealthy, must be part of broader deficit reduction to avoid the middle class from getting hit too hard.
Boehner met Thursday afternoon with Obama at the White House in their second face-to-face talks of the week. The two then spoke by phone on Friday, according to news reports.
CNN's Jessica Yellin and Brianna Keilar contributed to this report.