Efforts in the Senate to cut a last-minute bipartisan deal to avoid the fiscal cliff’s tax increases and spending cuts continued Sunday evening with little sign of an imminent breakthrough.

“There is still significant distance between the two sides, but negotiations continue,” Majority Leader Harry Reid, D-Nev., told senators just before 6 p.m. “There is still time left to reach an agreement, and we intend to continue negotiations.”

At least one issue appeared settled after senators emerged from late afternoon party caucuses. There was general agreement that a proposed change sought by Republicans in how cost-of-living increases are calculated for setting Social Security benefits and adjusting tax brackets is off the table in the current deficit-reduction talks.

The standoff on other issues continued with some $500 billion in tax increases due to take effect in barely more than a day.

Democrats said their latest proposal would extend expiring tax rates for individuals with taxable income up to $360,000 and couples with income of about $450,000.

Sen. Barbara A. Mikulski, D-Md., said revenue raised by allowing tax rates to rise for taxpayers above those levels would either pay for a two-year delay in the automatic spending cuts due to begin in January or for a one-year moratorium coupled with a renewal of extended unemployment compensation that expires at year’s end.

Senators made clear after their conference meetings that deep differences continue to separate the two parties on the estate tax as well as the automatic spending cuts.

While Democratic leaders are trying to implement President Barack Obama’s proposal to allow the estate tax rate to increase from 35 percent to 45 percent, Republicans continued to insist on the current rate.

Democrats pressed to defer the automatic spending cuts, perhaps for two years. But Republicans pressed to reconfigure the spending cuts instead of using tax revenue to replace them.

“The proposal for a two-year moratorium on sequestration is a sticking point,” said Kay Bailey Hutchison, R-Texas. She said the sequester should be held off, but for a shorter period.

A number of Republicans including John McCain of Arizona and Roger Wicker of Mississippi confirmed that Republicans have backed away from an earlier proposal to replace some of the spending cuts with savings from using the less-generous adjustments to Social Security, known as the “chained CPI.”

Obama caught flak from members of his own party when he included the new adjustment formula as part of his proposal for a longer-term deficit reduction deal earlier this month. Democrats say chained CPI would only be considered as part of an agreement that included an increase in the government’s borrowing limit, but Republicans do not want the debt ceiling on the table in the current negotiations. Republicans have made clear they hope to use a debt limit increase as leverage to win additional spending cuts early next year.

Charles E. Schumer of New York said Sunday morning that four sticking points included the income threshold for tax cut extensions, the estate tax rate and exemption level, a renewal of extended unemployment benefits and the automatic spending cuts put in place by the 2011 debt deal (PL 112-25).

Sen. Lindsey Graham, R-S.C., said he opposed including chained CPI in a fiscal cliff deal and said an agreement can be reached without such a provision. “It is not a condition of this deal for me and most Republicans to adjust CPI. I don’t know where that came from,” he said. “There is a crucial mass of 80 senators who would vote to fix the [alternative minimum tax], the doc fix, extend unemployment insurance, protect everybody $500,000 and below from a tax increase. There’s 80 senators that will do that without CPI.”

If no deal is reached, Reid has said he will ask the Senate to vote Monday on a tax package reflecting Obama’s proposals. Such a bill would extend current tax rates on income below $250,000 for couples, index the alternative minimum tax to inflation for 2012 and prevent payment cuts to physicians and tax estates at 2009 levels, with a top rate of 45 percent and a $3.5 million exemption.

On the House side of the Capitol, there was little expectation that there would be a vote on any potential deal Sunday. House GOP leaders planned to brief their conference Sunday evening.

It also appears more likely that House GOP leaders may prefer not to vote on any deal until Jan. 2, when any agreement would technically represent a tax cut after rates go up on Jan. 1. A lobbyist with knowledge of the negotiations said he has heard that the GOP does not want to vote on a plan until the new year.

In a note to lawmakers last week, House Rules Committee GOP aides cautioned that “given the realities of the legislative process, it would be very hard [though not impossible] to consider a deal this year. However, we stand ready to meet on whatever legislation is needed through the end of the year and beyond.”

Paul M. Krawzak and Sam Goldfarb contributed to this report.