A deal to avert the fiscal cliff at the end of the year will ultimately come down to talks between President Barack Obama, Speaker John A. Boehner and a handful of other top leaders — and this week may be one of the few times rank-and-file members are asked to weigh in.

Democratic and Republican leadership aides said there is at least some initial optimism that a deal can be reached, given that both Obama and Boehner, R-Ohio, offered olive branches last week in their initial post-election statements on the issue. But it now appears that agreement will have to emerge from just the kind of “Camp David” leadership retreat that Boehner last week said he wanted no part of.

Boehner and Democratic leaders know they have to get their respective rank-and-file members in line so they can find room to negotiate. So this week they will take the temperatures of their respective caucuses on taxes and entitlements, putting hard negotiations on hold until Friday, when they’re scheduled to meet at the White House.

Before they are asked to vote on any deal, members shouldn’t expect many chances to amend it in committee or on the House and Senate floors, despite its potential magnitude.

“This is going to be, as these things tend to be, a top-down kind of thing,” a Senate Democratic leadership aide said. “It is not going to be an inclusive legislative process. It’s going to be, ‘This is the deal, yes or no.’”

To be sure, leaders of both parties need some level of permission from the rank and file to sit down and negotiate. That will take some delicate footwork with hardliners on each side.

“In a certain sense, both sides have to speak to their base but also use language that leaves open the possibility of common ground more in the middle,” a House GOP leadership aide said.

Congressional leaders also will have plenty of opportunities this week to posture in the press, and Obama plans to hold a press conference of his own Wednesday. Democratic aides expect the president to enlist the business community to help nudge Republicans toward a deal, given the cliff’s potential risks to the economy and financial markets.

At issue for both Congress and the White House is how to deal with the Bush-era tax cuts, $1.2 trillion in scheduled automatic cuts to defense and non-defense programs, and a need to raise the debt ceiling.

Obama, for his part, has signaled a willingness to bend a little in the GOP’s direction.

“He used the word ‘revenues’ and not rates, and that was encouraging,” the House GOP leadership aide said of Obama’s demand that taxes go up on the wealthy. “No one underestimates the difficulty of working out the details here, but I think the last four or five days have been more positive than negative.”

Still, differences between even the leaders and White House will be hard to bridge. Republican aides say the White House needs to come through with serious entitlement reforms as well as work within Boehner’s bottom line of letting the top tax rate rise beyond the Bush-era rate of 35 percent. “The more real you can make it, that you are making real and lasting reforms to entitlements, the easier it should be to sell,” the GOP aide said of Boehner’s conference.

Republicans are waiting to see whether rank-and-file Democrats might be willing to swallow items like an increasing the Medicare retirement age to 67 — something that was on the table during debt limit talks a year ago — or slowing cost-of-living adjustments under Social Security, which Senate Majority Leader Harry Reid, D-Nev., has opposed.

Meanwhile, Democrats question whether Boehner can find the votes for any package before hitting the cliff Jan. 1, when pressure will ramp up on Congress as citizens’ taxes go up.

Democrats, including Sen. Charles Schumer of New York, have questioned whether Republicans can find a palatable alternative way to raise taxes on the wealthy without raising rates. Other Democrats, including Rep. Chis Van Hollen of Maryland, have said they are convinced the Republicans will ultimately have to give in on Democratic demands to hike taxes on the wealthy rather than go over the fiscal cliff to protect the top 2 percent of taxpayers.

While some Democrats may be queasy about going over the cliff, most seem determined to use the moment of greatest leverage to finally raise taxes on the wealthy.

“There are a lot of Democrats who say, ‘Let’s go over the cliff,’” the Senate Democratic leadership aide said. “That’s the cover Republicans are going to need to cut a deal.”

Even if leaders all agree on Boehner’s preferred path of raising revenue without raising rates, there’s no easy way to make up the lost revenue Obama has demanded.

Letting the top two tax brackets rise, with the top rate hitting 39.6 percent, while also letting taxes go up on investment income and large estates, would raise $866 billion over 10 years, according to the White House. In the context of a large deficit reduction agreement, many Democrats would like to raise as much as $1.5 trillion over 10 years, but even raising $800 billion could be difficult without raising rates, experts say.

One idea, put forward by GOP presidential nominee Mitt Romney during his campaign and endorsed by GOP lawmakers would be to place a cap on itemized deductions to avoid political fights over individual preferences. Most of that money would come from people earning more than $200,000, but about 9 percent would come from households earning less than that amount. Obama has said he won’t raise taxes on those making less than $250,000.

Beyond its effect on middle-income earners, a wide range of tax policy experts note several potentially unattractive consequences of a deduction cap. Many taxpayers could claim deductions for state and local tax and mortgage interest payments, which would shrink incentives for charitable deductions.

Sam Goldfarb contributed to this report.

An earlier version of this article misstated whom President Barack Obama said he wouldn’t raise taxes on. Obama has said he won’t raise taxes on those making less than $250,000.