“Everyone’s talking about suburban female voters because they’re deciding elections,” said Olivia Perez-Cubas, a spokeswoman for the Winning for Women Action Fund, a political group dedicated to electing Republican women. “They’re a coveted demographic in elections, and policies like paid family leave are important to them.”

Paid leave, in general, is an easy sell with voters. Families need it — 72 percent of mothers and 93 percent of fathers with children at home are in the labor force — and a large majority of voters support it. But Americans, like their elected representatives, disagree on the details, particularly how to pay for it.

In the State of the Union, Mr. Trump called paid parental leave for federal workers, a Democratic initiative he signed into law in December, “a model for the rest of the country.” But it has almost nothing in common with any of the paid leave bills in Congress, including the one he endorsed. The leave for federal workers, which will start in October, is financed by the government, and workers pay nothing (this is similar to companies that voluntarily give employees paid leave).

There is one model of government-run paid leave that has already been successfully adopted in the United States. In eight states and the District of Columbia, paid leave has been financed by a small payroll tax increase, paid by employees and employers. This is also the model that Democrats have proposed for all Americans, in a bill called the Family Act.

The child tax credit is worth up to $2,000 per child. If the Trump-backed bill passed, the average worker with a new child could receive $5,000, and then collect $500 less in child tax credits each year for 10 years. Workers earning less than $11,000 a year, who don’t qualify for the full child tax credit, could also get up to $5,000, and pay it back over 15 years.

Under the Democrat-backed Family Act, average workers would pay an additional $120 in annual payroll taxes, according to analysis by Vicki Shabo, a senior fellow on paid leave policy and strategy at New America, a left-leaning policy group. If they took leave, they would receive $9,920 for 12 weeks. Those with income of less than $11,000 a year would receive two-thirds of their pay, roughly $1,840, and their payroll taxes would increase around $22 a year, according to the analysis.

So far, the Family Act has minimal Republican support, and the deal breaker is the tax increase. “A payroll tax increase is not going to be passed into law anytime soon,” Ivanka Trump said on Face the Nation on CBS in December.