Paid leave for new parents, long a Democratic cause, has become a Republican one, too. But policymakers don’t agree on what a leave plan should look like. Now some Republicans have a new idea: Let people collect Social Security benefits early to pay for time off after they have a baby.

Unlike some other proposals, this would require no new taxes. There’s a catch, though: Parents would have their Social Security benefits delayed when they retire to offset the costs.

Social Security has long been viewed as an untouchable part of the social safety net. By letting people tap it for parental leave, it would begin to feel more like an individual account — an idea conservatives have been trying to advance for decades.

The new parental leave plan comes from a right-leaning group called the Independent Women’s Forum, and its president, Carrie Lukas, who said Social Security was based on an antiquated idea of working life. “Women are a bigger part of the work force now, and they need support at different times of their lives rather than just starting at 67,” she said.

More broadly, Ms. Lukas has said that she hoped the proposal would “encourage an important mental shift” in the way people think about Social Security. If individuals view it as “property,” she reasons, it could lead to the embrace of personal accounts.

That reasoning is why some experts view the proposal as a backdoor way to try to curb the scale and cost of Social Security. They also said it could put women in a more precarious position in retirement, adding yet another financial penalty to the list that women pay when they become mothers. Women have lower earnings, smaller Social Security benefits and less financial security in retirement because they spend a disproportionate amount of time away from work to raise children, research shows. Drawing down their Social Security benefits early could compound the problem.

“Here you have a situation where women live longer, but they tend to live both sicker and poorer because of the caregiving they do,” said Debra Ness, president of the National Partnership for Women & Families, a nonprofit that champions women’s economic security. “With this proposal, we would be asking them to borrow against the already inadequate support they receive from Social Security.”

Senator Joni Ernst of Iowa, a supporter of the idea, said it would provide women with more financial security by encouraging them to stay in the work force after they have children. “I think about those women that will leave the work force because that’s their only option, and this provides them a way to take some time off, spend time devoted to their family and then return,” she said.

The new proposal is one of several being considered by Ivanka Trump and others in the White House to expand paid leave beyond the 13 percent of workers who have access to it through their employers.

They are studying if the Social Security Administration can be used to administer paid leave, according to people briefed on their discussions. It could allow people to collect payments early, as in the plan Ms. Ernst spoke of, or it could administer a new fund, perhaps financed by payroll taxes, an idea some Democrats have proposed. The administration’s goal is to get bipartisan support on what has historically not been a Republican issue.

Three Republican senators — Ms. Ernst, Marco Rubio of Florida and Mike Lee of Utah — announced this month that they supported the Social Security proposal, though they were still researching it and had not yet started writing a bill.

In a conference call, the senators praised the fact that the plan would not force businesses to provide leave, would not start a new government program and would not raise taxes.

But Mr. Lee also raised concerns about the underfunding of Social Security, and whether this would accelerate its decline. That is the most controversial aspect of the proposal, experts said, because it would apply more stress to a program that is already under pressure.

Starting in 2034, Social Security will be able to pay only 75 percent of scheduled benefits, according to the latest trustees report, unless taxes are raised or benefits are trimmed. And while the chances of passing any legislation in an election year are dim, the proposal introduces a new strain of thinking about what Social Security can be used for. Another legislator, Representative Thomas Garrett, a Republican from Virginia, recently introduced a bill that would let individuals draw Social Security benefits early to pay off a portion of their student loans.

Millions of retirees rely on modest checks from the program, which was created from a bill signed into law by Franklin D. Roosevelt in 1935. Treating Social Security as something that can be borrowed against suggests that it can be treated as an individual account rather than a social insurance program. That could open the door to privatizing the accounts, some experts said, an idea that was floated during George W. Bush’s administration.

“This is a significant philosophy shift that doesn’t look at it like an insurance program where we are all in it together, but an individual asset you can tap to pay for your individual needs,” said Kathleen Romig, senior policy analyst at the liberal-leaning Center on Budget and Policy Priorities.

The proposal would also begin to reshape Social Security into something more akin to 401(k) accounts: Account holders can borrow against their 401(k), or even drain it in a financial emergency (albeit with a penalty), leaving them with less savings for retirement.

Social Security, in contrast, cannot be touched and is often viewed as the last standing leg in the three-legged stool of retirement, when personal savings are not enough and pensions are increasingly rare.

To be eligible for the proposed program, a new parent would need to have a minimum amount of earnings in the years before claiming the benefit, similar to the formula used to qualify for Social Security disability benefits, according to the proposal from the Independent Women’s Forum.

The size of the benefit would be calculated borrowing a formula from Social Security. A 26-year-old woman earning $31,000, for example, might receive roughly $1,175 a month in Social Security parental benefits, which replaces about 45 percent of her income, for up to 12 weeks.

The cost would come later, in the form of a reduced retirement benefit. Exactly how the reduction would be calculated is not yet entirely clear, said Andrew Biggs, a former principal deputy commissioner of the Social Security Administration who helped devise the proposal and who is now at the American Enterprise Institute, a conservative think tank. But roughly speaking, he said, a 12-week leave would most likely translate to a benefit cut of 1.5 percent.

The proposal says that a parent’s Social Security check would be delayed, not cut, to offset the amount gained during the paid leave.

Ms. Lukas said that delaying Social Security would not be a problem for most people: “Sixty-seven is really late middle age, and many people are really happy to continue working.”

Yet many workers do not have a choice. And while life expectancies have increased, better-paid and more educated people tend to live longer than those who earn less.

As of now, the proposal covers new parents but not workers who are recovering from an illness or need to care for other family members. It also does not provide job security for people who take leave. The Family and Medical Leave Act does both those things, but the leave is unpaid, and only about half of workers qualify for it.

The Family Act, a bill sponsored in the Senate by Kirsten Gillibrand, Democrat of New York, would create a new fund within the Social Security Administration. Employers and employees would each contribute 0.2 percent of their wages for 12 weeks of paid parental, family or medical leave.

Republicans generally object to proposals that would raise taxes, but any paid leave plan would need to be paid for. The question now facing policymakers is whether to turn to Social Security payments, the last guaranteed safety net for many retirees, to do so.