WASHINGTON — The end game at hand, the White House and Senate leaders made a final stab at compromise Friday night to prevent middle-class tax increases from taking effect at the turn of the new year and possibly block sweeping spending cuts as well.

“I’m optimistic we may still be able to reach an agreement that can pass both houses in time,” President Barack Obama said at the White House after meeting for more than an hour with top lawmakers from both houses.

Surprisingly, after weeks of postelection gridlock, Senate leaders sounded even more bullish.

The Republican leader, Sen. Mitch McConnell of Kentucky, said he was “hopeful and optimistic” of a deal that could be presented to rank-and-file lawmakers as early as Sunday, a little more than 24 hours before the year-end deadline.

Said Majority Leader Harry Reid: “I’m going to do everything I can” to prevent the tax increases and spending cuts that threaten to send the economy into recession. He cautioned, “Whatever we come up with is going to be imperfect.”

House Speaker John Boehner, a Republican who has struggled recently with anti-tax rebels inside his own party, said through an aide he would await the results of the talks between the Senate and White House.

Under a timetable sketched by congressional aides, any agreement would first go to the Senate for a vote. The House would then be asked to assent, possibly as late as Jan. 2, the final full day before a new Congress takes office.

Officials said there was a general understanding that any agreement would block scheduled income tax increases for middle class earners while letting rates rise at upper income levels.

Democrats said Obama was sticking to his campaign call for increases above $250,000 in annual income, even though in recent negotiations he said he could accept $400,000.

The two sides also confronted a divide over estate taxes.

Obama favors a higher tax than is currently in effect, but one senior Republican, Sen. Jon Kyl of Arizona, said he’s “totally dead set” against it. Speaking of fellow GOP lawmakers, he said they harbor more opposition to an increase in the estate tax than to letting taxes on income and investments rise at upper levels.

Also likely to be included in the negotiations are taxes on dividends and capital gains, both of which are scheduled to rise with the new year. Also the alternative minimum tax, which, if left unchanged, could hit an estimated 28 million households for the first time with an average increase of more than $3,000.

In addition, Obama and Democrats want to prevent the expiration of unemployment benefits for about 2 million long-term jobless men and women, and there is widespread sentiment in both parties to shelter doctors from a 27 percent cut in Medicare fees.

The White House has shown increased concern about a possible doubling of milk prices if a farm bill is not passed in the next few days, although it is not clear whether that issue, too, might be included in the talks.

One Republican who was briefed on the White House meeting said Boehner made it clear he would leave in place spending cuts scheduled to take effect unless alternative savings were included in any compromise to offset them. If he prevails, that would defer politically difficult decisions on curtailing government benefit programs like Medicare until 2013.  

Success was far from guaranteed in an atmosphere of political mistrust — even on a slimmed-down deal that postponed hard decisions about spending cuts into 2013 — in a Capitol where lawmakers grumbled about the likelihood of spending the new year holiday working.

In a brief appearance in the White House briefing room, Obama referred to “dysfunction in Washington,” and said the American public is “not going to have any patience for a politically self-inflicted wound to our economy. Not right now.”

If there is no compromise, he said he expects Reid to put legislation on the floor to prevent tax increases on the middle class and extend unemployment benefits — an implicit challenge to Republicans to dare to vote against what polls show is popular.

The president also booked a highly unusual appearance on Meet the Press for Sunday, yet another indication of his determination to retain the political high ground that came with his re-election.

The guest list for the White House meeting included Reid, McConnell, Boehner and House Democratic leader Nancy Pelosi, D-Calif.

The same group last met more than a month ago and emerged expressing optimism they could strike a deal that avoided the fiscal cliff. At that point, Boehner had already said he was willing to let tax revenues rise as part of an agreement, and the president and his Democratic allies said they were ready to accept spending cuts.

Since then, though, talks between Obama and Boehner faltered, the speaker struggled to control his rebellious rank and file, and Reid and McConnell sparred almost daily in speeches on the Senate floor. Through it all, Wall Street has paid close attention, and the meeting was still going on at the White House when stocks closed lower for the fifth day in a row.

The core issue is the same as it has been for more than a year, Obama’s demand for tax rates to rise on upper incomes while remaining at current levels for most Americans. He made the proposal central to his successful campaign for re-election, when he said incomes above $200,000 for individuals and $250,000 for couples should rise to 39.6 percent from the current 35 percent.

Boehner refused for weeks to accept any rate increases, and simultaneously accused Obama of skimping on the spending cuts he would support as part of a balanced deal to reduce deficits, remove the threat of spending cuts and prevent the across-the-board tax cuts.

Last week, the Ohio Republican pivoted and presented a Plan B measure that would have let rates rise on million-dollar earners. That was well above Obama’s latest offer, which called for a $400,000 threshold, but more than the speaker’s rank and file were willing to accept.

Facing defeat, Boehner scrapped plans for a vote, leaving the economy on track for the cliff that political leaders in both parties had said they could avoid. In the aftermath, Democrats said they doubted any compromise was possible until Boehner has been elected to a second term as speaker when the new Congress convenes on Jan. 3.

Further compounding the year-end maneuvering, there are warnings that the price of milk could virtually double beginning next year.

Congressional officials said that under current law, the federal government is obligated to maintain prices so that fluid milk sells for about $20 per hundredweight.  If the law lapses, the Department of Agriculture would be required to maintain a price closer to $36 of $38 per hundredweight, they said. It is unclear when price increases might be felt by consumers.