WASHINGTON -- President Barack Obama and congressional leaders were optimistic Friday after opening talks aimed at avoiding a tumble over the “fiscal cliff,” offering hints of a compromise that would combine new tax revenue with steep spending cuts.

Their hourlong meeting at the White House kicked off what’s likely to be an intense, unpredictable November and December as Congress and the White House grapple with how to deal with Bush-era tax cuts that expire at the end of next month and $109 billion in across-the-board spending reductions due to take effect Jan. 2.

Obama said after Friday’s meeting that they’d agreed to work together to find a solution that “includes both revenues and cuts in spending.” The challenge, he said, was to cooperate, “work together, find some common ground, make some tough compromises.”

House Speaker John Boehner, R-Ohio, and Senate Minority Leader Mitch McConnell, R-Ky., who’ve been loath to consider tax increases as part of a solution to tame the deficit, said after the closed-door meeting that Republicans might consider taxes if they were accompanied by significant spending reductions.

“We are prepared to put revenue on the table, provided we fix the real problem,” McConnell said, adding that most of his caucus thinks that “we’re in the dilemma we’re in not because we taxed too little, but because we spent too much.”

Back at the Capitol, the mood among Congress’ rank and file was largely conciliatory. But there was a sharp reminder that getting a deal through the lame-duck session faces a struggle with each party’s ideological wing, where some members dug in Friday.

“This was a photo op for the president. So be it,” said Rep. Tom Price, R-Ga., a leading conservative.

Among liberal Democrats, Rep. Jim McGovern of Massachusetts warned that “it would be foolish to just assume we’re to go along with everything. We’re not a cheap date.”

Liberals are thought to control as many as 90 Democratic seats in the House of Representatives, while staunch conservatives usually can count on about the same number on the Republican side. Each bloc has firm ideas of what it wants.

Conservatives insist that tax rates remain the same or go lower.

“We got a loud and clear message from the voters,” said Rep. Steve Scalise of Louisiana, the incoming chairman of the Republican Study Committee, the House’s conservative caucus. “The president only defines revenue as raising taxes. We see revenue coming from getting the economy moving again.”

Boehner was more circumspect, saying that Republicans put revenue on the table to demonstrate their seriousness about a solution. Boehner told Obama that without significant tax and entitlement changes, lawmakers will be unable to control the burgeoning budget deficit.

The speaker suggested that tax and entitlement issues may be too complex to solve in a lame-duck session. Negotiators should settle on long-term revenue targets for tax revisions, he proposed, as well as goals for savings from entitlement programs, such as Medicare.

Liberals said they were wary of big spending cuts, particularly those that hurt the poor or significantly cut Medicare.

Both sides in the talks have been open to raising the eligibility age for most Medicare recipients from 65 to 67, but Rep. Peter Welch, D-Vt., cautioned that “This is where the talks are going to get very difficult. There’s going to be a desire to shift the burden to beneficiaries.” The nonpartisan Congressional Budget Office has said that raising the eligibility age would save about $148 billion over 10 years.