With President Obama seeking a deal to avoid the “fiscal cliff,” liberal groups that campaigned aggressively for his reelection are mobilizing to oppose concessions they fear he could make on Medicare and Social Security.

Leaders of the nation’s labor unions and other liberal groups are planning Tuesday to press Obama at the White House to reject the kind of cuts in Medicare and Social Security that he has previously offered to make. On Thursday, left-leaning lawmakers and seniors groups plan to rally on Capitol Hill against any changes to entitlements.

Republicans are demanding entitlement changes as part of any deal to reduce the federal deficit. Top GOP lawmakers have said they could agree to raise fresh tax revenue — taking a step closer to the Democratic position that the wealthy pay more — but only if the White House accepts the type of entitlement changes that many liberals abhor.

During debt negotiations with House Speaker John A. Boehner (R-Ohio) in summer 2011, Obama tentatively agreed to increase Medicare premiums and later boost the eligibility age for the program from 65 to 67. He also was willing to modestly reduce Social Security payments by using a less-generous formula for making cost-of-living increases. After those talks collapsed, Obama did not include similar proposals in his debt-reduction plan released last fall.

Now, with negotiations resuming, Obama has not made clear precisely how far he would go on entitlements. But people close to the White House say officials believe the election strengthened their hand and reduced the need to make concessions. The extent of any entitlement changes may depend on how much new tax revenue Republicans are willing to accept.

In the negotiations, Obama may have to decide whether he is willing to break with his liberal allies in pursuit of a bipartisan agreement aimed at avoiding the year-end fiscal cliff — $500 billion in automatic tax hikes and spending cuts that many economists say could plunge the nation into recession.

“We will make it very clear we will not be supportive of cuts to Medicare and Social Security,” said Sen. Bernard Sanders (Vt.), an independent who caucuses with the Democrats. “It would be a huge shock and disappointment if the president forgot the reality that he just won a major victory.”

The White House decision to invite labor and other liberal leaders to a meeting comes as the debate over the fiscal cliff is escalating. On Wednesday, Obama is set to meet with business leaders who support a deal that increases taxes on the wealthy, and on Friday he will open discussions with congressional leaders in a meeting at the White House. High-level talks are likely to intensify after Thanksgiving.

The White House has suggested that if the talks do not progress as Obama wants, he may barnstorm around the country to rally the public behind his position.

Much of the public dispute over the fiscal cliff has centered on the president’s demand that taxes rise for the wealthy. But entitlements are an essential element of the discussion because they are the main drivers of the nation’s borrowing problem over the years to come.

Spending on Medicare and Medicaid is projected by the Congressional Budget Office to equal 10 percent of the economy in 25 years — double the percentage today. Over the same period, Social Security spending is expected to rise from 5 percent of the size of the economy to 6 percent, mainly as a result of the retirement of baby boomers.

“This is year two of a 25-year demographic bubble that it wasn’t like anyone couldn’t see it coming,” Boehner said Friday. “This has to be dealt with. So everything — everything — on the revenue side and on the spending side has to be looked at.”

Democratic lawmakers have made clear they will oppose any changes to Social Security. Last week, Senate Majority Leader Harry M. Reid (D-Nev.) told reporters that he is open to a fiscal-cliff deal but that “we are not going to mess with Social Security.”

Obama’s 2013 budget would reduce spending on health-care programs by $360 billion over a decade, in part by reducing payments to drug companies. Obama has also proposed increasing premiums for some retirees starting in 2017.

“There’s a lot of mobilization going on to try to prevent any cuts in social insurance benefits,” said Larry Mishel, president of the liberal Economic Policy Institute. “I’m hoping they don’t go back to what they were offering up in 2011.”

Jared Bernstein, a former White House economic adviser with close ties to liberals, said revisions to entitlements that strengthen the programs would be acceptable if the poorest people were not harmed.

“It’s reasonable to put the entitlements on the table but in such a way that protects economically vulnerable people who depend on them — which is a much larger group than you might think,” he said. Bernstein noted that the median income of a Medicare beneficiary is $22,000 per year.

Neera Tanden, president of the Center for American Progress, said liberals understand the need to slow Medicare spending but want to do it carefully.

“But we have to be really mindful of where those savings come from and whether they’re coming out of the pockets of seniors and whether they’re the result of savings in the health-care system,” Tanden said. “Those are two different things, and one progressives can agree with, and one is extremely difficult.”

Other liberals say they will fight against any entitlement beneficiary cuts. The AFL-CIO kept its field organizers active for a week after the election to lobby lawmakers against entitlement cuts, while MoveOn.org is using its e-mail list of 7 million people to mobilize.

“We will give the president and his allies in Congress all the support and cover in the world in the fight for no more tax cuts for the rich. That includes, in particular, supporting the president’s position that it’s better to negotiate past December 31st than do a deal that’s bad for the country,” said a top labor official who spoke on the condition of anonymity to comment ahead of Tuesday’s meeting. “On the other hand, the answer for those who want to cut social insurance benefits in an economic crisis and increase economic insecurity is, ‘Hell, no.’ ”