By Yamiche Alcindor

WASHINGTON — Two days before Election Day, Donald J. Trump traveled to Sioux City, Iowa, and proclaimed that he was the protector of federal programs aimed at helping elderly and low-income Americans. It was Hillary Clinton, he said, who was an untrustworthy steward of the working class and who would slash vital benefits.

“I am going to protect and save your Social Security and your Medicare,” Mr. Trump said. “You made a deal a long time ago, a long time ago.” The pledge followed earlier promises to enact a new paid-maternity-leave benefit and not to make cuts to Medicaid, the health insurance program for the poor.

When President Trump addresses Congress this Tuesday and follows the speech with a budget blueprint for the fiscal year that begins in October, his White House will finally address in concrete numbers one of his central contradictions: He campaigned as the populist protector of programs for the working class, yet he has pledged to control the budget deficit, cut spending and cut taxes.

Moreover, Mr. Trump has surrounded himself with traditional small-government conservatives bent on cutting back or eliminating many of the programs he has championed. Many of his aides and cabinet members have expressed views that are fundamentally opposed to those he campaigned on.

Former Representative Mick Mulvaney of South Carolina, for example, the new White House budget director, has called Social Security a “Ponzi scheme” and helped engineer a government shutdown to cut spending. As House Budget Committee chairman, Tom Price, the new secretary of health and human services, supported converting Medicaid to strictly capped block grants to the states and turning Medicare into a voucherlike program for future recipients. Ben Carson, the president’s nominee to head the Department of Housing and Urban Development, has repeatedly said government programs to help the poor lead to dependency.

The disparity between Mr. Trump’s rhetoric and his appointments has cheered many Republicans and left Democrats fearing that he will not only renege on his promises to protect the government’s largest entitlement programs but that he will also slash programs he did not mention on the campaign trail that offer food, housing and child care support for the poor.

“The appointments that he’s made are troublesome and very, very scary,” Senator Al Franken, Democrat of Minnesota, said. “He made a pledge and sort of delineated himself from the rest of the Republican field by saying these things. Everything he’s done since he’s been elected is very worrisome.”

Already, Mr. Trump’s budget office has hinted at cuts to come in a memo that singled out the Legal Services Corporation, which helps the poor manage legal issues, and the Appalachian Regional Commission, which targets economic development in some of the poorest parts of the country. The memo also said that AmeriCorps, a program that puts volunteers into poor communities, would be zeroed out, and that the Neighborhood Reinvestment Corporation, a nonprofit organization focused on urban development, would see its budget cut substantially.

On Capitol Hill, some Republicans are hoping Mr. Mulvaney and others will change the president’s mind on far bigger targets and convince him that structural changes to Social Security, Medicare and Medicaid — the biggest drivers of deficits that are projected to rise over the next decade — are needed to control the national debt and to preserve the programs without substantial tax increases.

Social Security, Medicare and Medicaid consumed nearly $1.9 trillion of the government’s $3.9 trillion in spending in 2016, according to the Congressional Budget Office, and with the number of people 65 and over projected to rise by a third over the next decade, Social Security and Medicare spending is projected to increase from a third of all spending in 2017 to 42 percent by 2027. Including Medicaid and military and federal civilian retirement benefits, federal spending on older adults will rise from 37 percent of outlays in 2017 to 45 percent in 2027 if nothing is done to change the programs.

Even some liberal economists say that will amount to a transfer of funds from poor children and families toward better-off older Americans, because the budget office projects that discretionary spending — where most programs for poor families come from — will be squeezed from 6.3 percent of the economy now to 5.3 percent in 2027, the smallest level since 1962.

With those numbers on their side, Republicans are most likely to use their power in both the executive and legislative branches to push through large cuts to federal programs for poor and working-class Americans, say Democrats and liberal policy analysts — if Mr. Trump eases up on his promises.

“This is the greatest threat to low-income people in my lifetime,” said Olivia Golden, executive director of the Center for Law and Social Policy, a nonprofit organization focused on low-income Americans.

House Republican allies see no real contradiction in Mr. Trump’s campaign promises and what they say he must now do. Since President George W. Bush’s failed 2005 effort to partially privatize Social Security, Republicans have assured retirees and those nearing retirement that any changes or cuts to entitlement programs for older adults would not affect them.

Now, Republicans are retroactively applying those caveats to Mr. Trump’s promises, saying the president understands that programs like Social Security and Medicare must be maintained for Americans who are currently receiving benefits but must be changed for younger Americans who may have to work longer before retiring and getting benefits.

“It was really about making sure that those people who are getting benefits or about to get benefits are protected,” said Representative Mark Meadows, Republican of North Carolina and a leader of the hard-line conservative House Freedom Caucus. “If we do nothing, he will not save Medicare and Social Security.”

Representative Jeff Duncan, Republican of South Carolina, said he would be closely watching his former Freedom Caucus colleague, Mr. Mulvaney, as he settles in to work at the Office of Management and Budget. “I’m curious to see how Mick Mulvaney approaches this from O.M.B. because he is very like-minded with us here,” Mr. Duncan said.

In fact, on the campaign trail and in interviews before the election, Mr. Trump did not suggest that he would maintain the programs in their current form only for older Americans. His rallies were attended by a cross-section of ages, who cheered his broad promises. And last March, Mr. Trump said during a debate among Republican presidential candidates that he planned to make no changes.

“I will do everything within my power not to touch Social Security, to leave it the way it is,” Mr. Trump said. “I want to leave Social Security as is, I want to make our country rich again so we can afford it.”

The pressure to break that promise will come not only from congressional Republicans but also from his own campaign pledges to build a wall along the Mexican border, increase spending on defense, border security and infrastructure, cut taxes “big league” and control the deficit.

“The last time we saw this kind of budgetary logic was at the beginning of the Reagan administration when he came into office, pledged to beef up defense spending and cut taxes,” said William A. Galston, a senior fellow at the Brookings Institution and a former aide to President Bill Clinton. “They tried to keep the spending increases down and the deficit increases down by whacking away at social safety net programs, many of which were cut during that period.”

Even if Mr. Trump keeps his promise not to touch Social Security and Medicare, other programs like housing subsidies, child care assistance, the Supplemental Nutrition Assistance Program, also known as food stamps, could be cut, social welfare and budget analysts say.

And those cuts would not just affect poor minority voters, who tend to support Democratic candidates. A study released this month by the liberal-leaning Center on Budget and Policy Priorities research group shows that white working-age adults without a college degree, a critical voting block for Republicans, benefit the most from social safety net programs and poverty-reducing benefits.

“My fear is that we are going to see the biggest cuts that any president has ever proposed in programs for low- and modest-income families,” said Bob Greenstein, the center’s president. “It could be the biggest Robin Hood in reverse a president has ever offered.”