By Louise Radnofsky

WASHINGTON, D.C.—As Republicans near the finish line on a long-sought tax overhaul, President Donald Trump has committed them to taking up a welfare-revamp fight next.

Mr. Trump has repeatedly said he is interested in kick-starting a debate around means-tested social programs, with allies seeing significant political rewards from taking up the issue even without a clear-cut goal.

“Does anyone want welfare reform?” Mr. Trump asked, to applause, at a speech in Missouri last week. “And infrastructure. But welfare reform, I see it, and I’ve talked to people. I know people that work three jobs and they live next to somebody who doesn’t work at all.”

He added: “And the person who is not working at all and has no intention of working at all is making more money and doing better than the person that’s working his and her ass off… So we’re going to go into welfare reform.”

The president didn’t offer specifics about which of the dozens of welfare programs he was seeking to change, or how. But congressional Republicans who have been pushing him for months to pursue the issue have proposed layering tougher work requirements on beneficiaries of programs such as food stamps, which are used by around 43 million Americans, and the cash benefit known as Temporary Assistance for Needy Families, which is received by around 3.5 million people.

Such proposals have been floated in House Speaker Paul Ryan’s “A Better Way” plan, which included a broader call to review the ways in which welfare programs interact, as well as bills from lawmakers such as Rep. Jim Jordan (R., Ohio), who also has proposed tallying spending on all welfare programs.

A spokesman for Mr. Ryan said the goals for 2018 would be set at a conference retreat in January. But Mr. Jordan, a head of the conservative House Freedom Caucus who often has the ear of the president, has argued in recent weeks that the issue is one of the most winning ones with Mr. Trump’s voters and should take center stage next year.

He said he and fellow conservative Rep. Mark Meadows (R., N.C.) had made a pitch to the president to pursue welfare as an issue in a meeting in the early summer.

“He gets it,” Mr. Jordan said. “I think there are lots of folks across the country who get it, but particularly in Pennsylvania, Ohio, Michigan, Wisconsin, folks understand that they’re working hard, doing what’s right for their family, and there are folks who can work, and won’t work, and they’re getting their money.”

Democratic lawmakers have indicated they are ready for a fight, in which they will argue proposals to change assistance programs are a sign of misplaced priorities by Republicans who favored the rich in the tax overhaul.

“Republicans are already saying ‘entitlement reform’ and ‘welfare reform’ are next up on the docket,” said Sen. Ron Wyden (D., Ore.) in a Senate floor speech. “But nobody should be fooled—that’s just code for attacks on Medicaid, on Medicare, on Social Security, on anti-hunger programs. The story will be that America can’t afford these programs.”

Mr. Trump also has signaled his intention to simultaneously pursue infrastructure and a renewed effort to overturn the Affordable Care Act after any tax overhaul is complete. His advisers have made clear in unusually public ways that they are ready to move ahead on welfare.

A draft executive order has been prepared during the past two months for Mr. Trump to sign, at the president’s request, said Paul Winfree, Mr. Trump’s domestic policy council deputy at a November forum of the Heritage Foundation, a conservative think tank.

“It’s something that excites” Mr. Trump, who often changes the topic to discuss it in meetings, said Mr. Winfree, who worked for the foundation before he went to the White House. “We will end up pivoting to welfare very quickly.”

The order is expected to lay out broad principles for an overhaul of some or all of the dozens of federal programs that provide government aid to low-income people, with the aim of sending a clear message to Capitol Hill that changes are in order, Mr. Winfree said. The order also would include instructions for federal agencies to propose changes to the particular programs they oversee and craft new regulations, if necessary.

Such an order would be in keeping with many of the president’s policy moves in his first year in office—a broad-ranging order to initiate future action, or memos that simply preserve options down the line. Congressional leaders have been informed of the drive, Mr. Winfree said.

The president’s budget, expected in February, could include further details about his aims on a welfare overhaul and outline a cross-government approach, a senior administration official said. From there, the president would likely support any bill the GOP caucus in the House could agree to, the official indicated, and hope that the Senate was willing to pursue it.

In looking afresh at safety-net programs, the administration would face big questions, including which programs to deem as “welfare” and which beneficiaries to target for cuts or additional requirements.

Some of the programs with the smallest political constituencies, such as state grants for the Temporary Assistance for Needy Families programs, present few official savings in government spending because they are already capped. By contrast, large programs, such as unemployment compensation or food stamps, officially known as the Supplemental Nutrition Assistance Program, could trigger bigger political fights.

Democrats, in particular, are expected to quickly counter that much of what is considered welfare already comes with steep requirements, especially in the aftermath of the 1990s welfare-overhaul legislation, and that the beneficiaries to whom the requirements don’t apply are typically the elderly, disabled, or children. They have already challenged the Trump administration’s decision to allow states to add work requirements to Medicaid, the federal-state program for the poor, arguing they will be counterproductive.

Advocates say they are heartened by the response of voters in 2017 elections, including in Maine where voters backed a referendum on a federally funded expansion of the state’s Medicaid program.

“The Republican desire to take up ‘welfare reform’ is based on grossly inaccurate stereotypes about the workers, children, parents, and seniors who are helped by key programs such as SNAP and Medicaid and a complete misunderstanding of the realities of today’s labor market,” said Olivia Golden, executive director of the left-leaning Center for Law and Social Policy, and a Health and Human Services official during the Clinton administration.