Under the plan, individuals earning up to $250,000 a year, and couples earning up to $500,000, would be able to deduct from their taxable income the average cost of child care in their states. The benefit would be modest; for example, a reduction of $840 in federal taxes for a family earning $70,000 a year and paying $7,000 for child care. The plan would offer low-income workers child-care rebates, paid once a year through the earned-income tax credit. The proposal also calls for dedicated savings accounts in which families could invest pretax income to cover child care and elder care costs, as well as incentives for employers to provide child care in the workplace.

Those without wages, like unemployed single parents seeking work or attending job training, would not benefit from the Trump subsidies and are underserved by existing programs. The Child Care and Development Block Grant was created in 1996 as part of welfare reform and was intended to help the poorest parents afford day care. Those benefits currently reach only one out of every 10 eligible children, according to the National Association for the Education of Young Children.

Despite its limited reach, the Trump plan is expensive. An analysis by the Tax Policy Center found it would cost $115 billion over 10 years, most likely making it a nonstarter for Republicans. The proposal also offers little to the working poor, a potential problem for Democratic champions of child care, like Nancy Pelosi and Bernie Sanders. The average annual benefit would be just $10 for families earning $10,000 to $30,000 a year, according to the Tax Policy Center.

It is difficult to square President Trump’s child-care plan with his other budget priorities. Carrie L. Lukas, managing director of the conservative Independent Women’s Forum, supports Mr. Trump’s efforts to help families with child-care costs. But “he also talked about the need for tax simplification,” she said, “which is inconsistent with using deductions” as a social policy strategy.

Still, Ms. Lukas is enthusiastic about some aspects of the Trump proposal, including the fact that married couples with one stay-at-home parent would be able to claim the same tax deduction as many dual-income couples whose children are enrolled in child care. That is an unusual element of the plan; after all, parents who care for their children at home do not incur costs for day care tuition or nanny salaries.

Traditionally, many European nations that enacted government-supported child care had the goal of encouraging maternal employment. More working women means more tax revenue, and better, more accessible child care helps convince parents that they can afford to have more children, who in turn will become future taxpayers supporting the welfare state.

That is not a conservative vision. “It shouldn’t be about pushing to get people into 9-to-5 jobs and kids into day care,” Ms. Lukas said. “That’s not an appropriate role for government. I’ve got five kids, and there are a lot of nonworking parents in my community. They are not only taking care of their own kids, but they are volunteering at school.”