Updated

The post-election negotiations on U.S. deficit reduction that began with a surge of optimism sputtered this week with Republicans expressing political indignation over President Obama’s opening offer to keep a $500 billion mix of tax hikes and federal spending cuts from kicking in next month should no deal be reached.

“There has been no substantial progress over the past two weeks,” House Speaker John Boehner said Thursday at a press conference, adding to his daily reports that portrayed the closed-door negotiations as languishing.

A day later, the Ohio congressman and the Republicans' chief negotiator with the White House simply acknowledged talks had reached a “stalemate.”

Both sides now have 31 days to reach a deal before the Jan. 1 deadline, with the president saying he would like one before Christmas.

“Congress can … give families like yours a sense of security going into the New Year,” he said Saturday in his pre-recorded radio address.

Amid a near-consensus call to reduce the deficit through a combination of tax increases, to generate revenue, and cuts in such entitlements as Medicare and Social Security, to reduce spending, the White House made an opening bid Thursday that called for roughly $1.6 trillion in new tax revenue over 10 years – nearly double what was previously proposed.

Senate Minority Leader Mitch McConnell said he "burst into laughter"  at the offer as put forth on Capitol Hill by Treasury Secretary Tim Geithner, now helping lead negotiations.

The president’s plan also calls for $600 billion in savings from changes in mandatory spending programs including Medicare and $200 billion in spending -- ranging from public works projects to help for the unemployed and struggling homeowners, administration officials said.

As lawmakers prepared Sunday to return to Washington from Thanksgiving break, Republican leaders acknowledge the federal government needs more revenue to cut its roughly $16 trillion deficit and that party members to accomplish that goal might break from a decade’s-old pledge not to increase taxes.

However, as the week unfolded both sides appeared to dig in over the tax cut issue.

President Obama, fresh off re-election, remains steadfast that he will extend tax cuts only to families earning less than $250,000 annually.

The Boehner-led Republicans say letting the cuts expire for the remaining 2 percent of American who make more would be a crippling blow to the economy because many of them are small-business owners.

The president held a series of campaign-style event over the week to sell his plan and to attempt to portray Republican as trying to withhold the cuts for the middle class.

Speaking at a toy factory, Obama said allowing taxes to rise for the middle class would amount to a "lump of coal" for Christmas.