The Washington Post’s Chris Cillizza looks at the potential dealmakers in the “fiscal cliff” talks. (The Washington Post)

President Obama and House Speaker John A. Boehner are continuing their talks, but key officials in both parties now believe that Washington will be unable to avoid some mix of the tax increases and automatic spending cuts mandated next month by the austerity measures known as the “fiscal cliff.”

Senior Democratic and Republican officials say the best-case scenario will be for a less ambitious deal to extend middle-class tax cuts and forestall tax hikes on most Americans.

But such a deal would still set in motion a series of steep spending cuts at some federal agencies and allow key tax provisions to expire, raising taxes for many. “I don’t know if we fall off the cliff, but I think we’re at least going to jump out of a tree,” said Sen. Lindsey O. Graham (R-S.C.).

That assessment hasn’t stopped Obama and Boehner (R-Ohio) from trying to reach a broader pact before year’s end. The two spoke by phone Friday afternoon, after news broke of the massacre at an elementary school in Connecticut, and officials in both parties confirmed that Boehner was considering allowing tax rates to rise for those earning more than $1 million annually, in exchange for cuts in entitlement programs.

That would represent a significant concession for Boehner, who has opposed any increase in rates and warned that such a plan could not pass the GOP-dominated House.

But the White House, which wants higher rates on annual incomes above $250,000, rejected Boehner’s offer, according to officials familiar with the talks.

Obama, Democrats says, believes he has already won on this issue, having won reelection by campaigning on a pledge to raise taxes on the wealthy, which polls show that a majority supports.

Instead, congressional Democrats say, Obama is only prepared to discuss cuts to Medicare and Social Security if Republicans are willing to reform the process for lifting the Treasury’s borrowing authority, surrendering the GOP’s ability to use a debt-ceiling fight early next year as a leverage point for more spending cuts.

This standoff has left many leaders in both parties searching for fallback plans.

White House press secretary Jay Carney told reporters Thursday, “In case of emergency, the House should break the glass; the House speaker ought to allow the Republicans to vote on extending tax cuts for 98 percent of the American people. That would deal with a chunk of the so-called fiscal cliff.”

The hope is to blunt the impact on the economy of the more than $500 billion in annual automatic tax increases and spending cuts scheduled to take effect in January, and buy time into next year for a broader deal involving comprehensive reforms of the tax code and federal entitlement programs.

No new face-to-face negotiations are scheduled for Obama and Boehner. The speaker’s aides declined to comment on the issue of Boehner offering a tax hike on millionaires, which was first reported by Politico. “We have not commented on the content of private discussions, and we’re certainly not going to comment on rumors,” Michael Steel, Boehner’s spokesman, said in a statement.

Some senior Democrats now believe that a deal cannot be reached until January, after the new Congress is sworn in and Boehner is reelected as speaker, because allowing tax increases could spark a rebellion among conservatives and threaten Boehner’s hold on the gavel.

“I hope he wouldn’t avoid tough decisions simply to take us into January after his swearing-in, but I’m becoming increasingly worried that that’s exactly what’s going on,” Rep. Chris Van Hollen (Md.), the top Democrat on the House Budget Committee and a key White House ally, told reporters last week.

Senate Republicans have proposed several options that would meet the GOP’s political imperative to not vote to approve higher taxes. One idea is to have the House approve a Senate-passed plan that raises taxes on the top two income brackets and extends the middle-class tax cuts, while also approving a second bill that extends the tax breaks for the top 2 percent of income earned. The latter legislation would then die in the Democratic-controlled Senate.

Another idea is for the House to approve a bill extending all the tax breaks, but to allow the Senate to consider it in two parts and reject the tax cuts for the wealthy.

Even if a fallback plan is approved, the current payroll tax holiday will lapse, unemployment benefits will begin to expire for the longtime jobless and no remedy will be at hand for dealing with the roughly $100 billion in automatic spending cuts at federal agencies.

The only real consensus, to date, is that the Obama-Boehner talks have not produced enough progress. Sen. Ben Nelson (Neb.), a retiring centrist Democrat who has been a key dealmaker, described the negotiations as “languishing.” Freshman Rep. Blake Farenthold (R-Tex.) joked that he just wants a few days off over the holidays.

“I’m thinking if we get any time off for Christmas, I may go to Mexico and learn to cliff-dive,” he said. “I don’t want to see us go over the cliff. But the president has got to give something. And we’re not getting any give.”

Hovering over these negotiations are reminders of the summer of 2011, when Obama and Boehner tried in vain to craft a “grand bargain” that would have saved $4 trillion in spending over the next decade and allowed an increase in the federal debt limit.

In the current faceoff, Obama sees in Boehner an intriguing partner who wants to cut the big deal, but the president remains unsure whether the speaker can sell such a compromise to his skeptical conservative colleagues.

To Boehner, the president also seems willing to make a deal, but his aides say White House aides often back away from the boss’s positions in follow-up meetings.

“Our staff has learned it is important to ‘trust but verify’ — the president is often vaguely accommodating in conversations, but the detailed offers produced by his staff don’t seem to match his words,” a senior aide to Boehner said Friday, speaking on the condition of anonymity to talk freely about the negotiations.

The two men have been reluctant to fully engage, partly because of the lessons learned last year.

In a seven-day span in early July 2011, the president and speaker held two one-on-one meetings in the Oval Office, spoke three times by phone and met along with other congressional leaders at the White House twice, according to a tally kept by Boehner’s office. In the nearly six weeks since Election Day — when voters left Obama and Boehner in charge again — the two have met in person only three times. They spoke by phone a handful of times.

Part of this was by design. Two senior White House officials said that David Plouffe, Obama’s top political adviser, crafted a plan to keep the president from getting sucked into a long, public negotiation like the one that unfolded over the debt ceiling. They said that Obama’s lowest moments in his first term came in a six-month stretch of 2011 when he acted as negotiator-in-chief on the annual federal spending bills and the effort to lift the Treasury’s borrowing authority, becoming part of the image a dysfunctional Washington.

“The last thing we want is another month of images of the two of them negotiating,” one senior official said. The White House is determined that Obama “not be drawn to that level.”

Instead, Obama has done campaign-style events in swing states pitching what he calls a “balanced” plan including $1.6 trillion in new tax revenue, primed by allowing the top two tax rates to rise to their 1990s levels.

From the moment the White House announced plans for those events, in mid-November, Boehner and Republicans viewed the talks on the fiscal cliff with deep suspicion. Boehner tried to steer the discussion back to the same framework that he and Obama were hashing out in July 2011, with a revenue target of $800 billion and changes in entitlements that included raising the age eligibility for Medicare and decreasing the cost-of-living adjustment for Social Security beneficiaries.

But Obama said the entitlement discussion had to wait until Republicans agreed to raise tax rates on the top 2 percent of income, as he had campaigned on successfully in his reelection bid. The standoff settled along those lines until Sunday, when the president and Boehner held their first one-on-one meeting since the July 2011 talks. According to senior House Republican aides, Obama and Boehner discussed new figures for tax revenue. The speaker suggested he would increase his offer well above $800 billion if Obama yielded on entitlement reforms, and Boehner relayed to his leadership team that the president seemed inclined to offer $1.2 trillion in new tax revenue.

Instead, on Monday, White House aides sent the new offer, which included $1.4 trillion as the revenue target and no new moves on entitlements. The speaker’s aides have suggested that several similar moves happened in 2011, when Boehner felt Obama’s staff pulled a bait-and-switch on issues discussed between the two men, and that set off a new fury among Republicans that set the tone for a bad week in negotiations.

Rosalind S. Helderman, Karen Tumulty and Scott Wilson contributed to this report.