The Republican Party won the last election in no small part because of its new appeal with working-class voters, a shift that left many in Washington wondering if a sustained political realignment was afoot.

But the economic agenda Republicans are now putting together on Capitol Hill would by and large help rich Americans, all while teeing up cuts to programs that provide health care and food to the poor.

The disconnect has left some Republicans nervous about whether they are abandoning their newfound base of support. Democrats, eyeing that vulnerability, are hammering Republicans for planning to take from the poor to give to the rich, a line of attack that they believe helped lift them back into power during President Trump’s first term.

Who is helped and who is harmed by Republicans’ plans are shaping up to be central questions for G.O.P. lawmakers as they try to squeeze legislation through their narrow majorities in Congress. The House on Tuesday adopted a budget blueprint that calls for $4.5 trillion in tax cuts and $2 trillion in spending reductions, alongside $300 billion in new funding for defense and border programs and an increase in the debt limit.

The House vote was just the first step in what could be a circuitous path to turning the plans into law. The Republican Senate has its own ideas for the party’s agenda, and the two chambers will have to agree on the broad strokes of the legislation before they can proceed to passing it along party lines.

Some House Republicans who supported the budget outline this week said they hoped that the Senate would ultimately tear up their plans. Making the math work in the House plan would almost certainly require cuts to programs for the poor like Medicaid, which provides health care to more than 70 million Americans. Representative Jeff Van Drew, a New Jersey Republican, said he had pitched Mr. Trump on avoiding deep cuts to Medicaid.

“He does not want Medicaid cuts on hard-working people. He knows this is the new majority. It is the new majority of the Republican Party, and it’s the right thing to do,” he said. “The Senate is going to straighten it out.”

The difficulty springs from Republicans’ expensive tax agenda. However their plans evolve, they will want to cut taxes, and fiscal hawks in the party are demanding that they also cut spending to help fill that fiscal hole. Because the federal government most heavily taxes the rich and focuses much of its spending on the poor, broad cuts to both taxes and spending would be regressive, or advantaging the rich over the poor, analysts say.

“They’re cutting taxes in a regressive manner and cutting spending, which is also regressive,” said Kyle Pomerleau, who studies tax policy at the American Enterprise Institute, a conservative think tank.

The American tax system is progressive, with the top 1 percent of Americans paying more than 30 percent of the taxes the federal government collects every year, according to Treasury Department data. So tax cuts like the ones Republicans hope to enact would provide their largest benefits to rich Americans who pay the most in tax, meaning the policy is regressive even if it still returns money to the working class.

Consider the top Republican tax priority this year: continuing the tax cuts the party passed into law in 2017. Among the measures that expire at the end of the year are lower marginal tax rates across income brackets, an expanded standard deduction and a more generous child tax credit, which is aimed at low- and middle-income Americans.

Most Americans saw lower taxes because of the bill, and Republicans see it as a political imperative to keep the existing cuts in place. Doing so would offer comparatively little to poor Americans who do not pay much tax. An analysis from the Tax Policy Center, a think tank, showed that Americans in the bottom 20 percent of earners, who make up to $33,900, would see on average a 0.6 percent — or $130 — increase in their after-tax income if the tax cuts were extended.

That’s smaller than the 1.8 percent boost the think tank expects for Americans on average. And it is far smaller than the 3.2 percent, or $70,350, increase in after-tax income that extending the tax cuts would provide to the top 1 percent, who make more than $1 million a year.

Republicans are considering additional tax cuts that could provide even more benefits to high-income Americans. Even corporate tax breaks that help grow the economy still flow mainly to the owners of businesses, who are typically wealthy.

Another idea under consideration would be to lift a $10,000 cap on state and local tax deductions that was put in place as part of the 2017 tax cuts. Any increase in the so-called SALT deduction would accrue to higher-income Americans who may owe a lot of property taxes on their valuable homes, for example.

Republicans defend their tax plans, which they argue can help grow the economy and in turn help lift wages for working-class Americans. Representative Jodey C. Arrington, Republican of Texas and the chairman of the House Budget Committee, believes that pairing spending cuts with tax cuts can juice the economy by reducing the amount the federal government has to borrow to pay for the tax cut.

“So if you are cutting taxes, they’ll say that the crowding out of private capital because you are borrowing more will kind of offset some of the positive economic growth potential that will come from lowering taxes,” he said this week. “But when you’re cutting spending, you’re reducing that crowding-out effect.”

Because their plans are still preliminary, Republicans have not yet detailed how they will achieve the spending cuts called for in the House budget blueprint. They have said they do not want to take away health care from children and other vulnerable Americans, though many of them appear open to rescinding enhanced federal aid for adults covered by the expansion of the program under the Affordable Care Act.

Under that law, the federal government pays for much of the cost of providing care to Americans who earn up to 138 percent of the federal poverty level, equivalent to $20,780 for an individual or $35,630 for a family of three, according to the Center on Budget and Policy Priorities, a liberal think tank.

Republicans are debating cutting the amount of money the federal government gives to states to provide health care to those people, a change that could endanger coverage for more millions of such Americans. For low-income Americans, the loss of Medicaid would likely be a greater loss in value than any gains provided by a cut in their income taxes.

“Cuts to Medicaid, for low-income and moderate-income families, are likely to overwhelm any tax cut that they get,” Brendan Duke, the senior director of federal fiscal policy at the Center on Budget and Policy Priorities, said.

During the campaign, Mr. Trump proposed a slew of novel tax policies that were targeted at working-class voters, including ending taxes on overtime, tips and Social Security. Republican lawmakers are not sure if they can find the money to afford several of those ideas, which in any case may not do much to help low-income Americans who don’t owe income taxes.

For some Republicans, pursuing an agenda that cuts taxes and spending is frustrating, given the way the party’s support has changed over time. Such an agenda may have made some political sense back when Republicans received more of their support from rich Americans. Not anymore, said Oren Cass, a founder of the think tank the American Compass and a leading voice in the so-called New Right.

“They have this old script they think they’re supposed to be reading off that says we’re going to cut taxes for high-income families and cut benefits for the poor,” he said. “That was always an incredibly dumb script, but it was one that the Republican Party thought it should be pursuing once upon a time. And now the Republican Party doesn’t think they should be pursuing it, but they’re still blindly wandering forward as if that’s what they’re supposed to do.”