"The fact you have to pay it back is unusual," Johnson said. It raises questions about who should share in the cost of raising children.
Paid leave should be a benefit provided by employers, says Jennifer Himes, a customer service rep in Pittsburgh . "This is a scam to take your own money out of your retirement fund," she said, "thus lowering the amount of money you will have at retirement."
The burden of repayment would fall disproportionately on poorer families and women, says Johnson.
Freelance workers will also take a financial hit. "Lots of people are freelancing at things you don't think about," said Rebecca Sommerhauser, 54, who lives in St. Louis, such as the grocery delivery service Shipt, or driving services like Uber and Lyft.
More from Personal Finance:
Here's how to protect yourself from sexually transmitted debt
If you spent too much this summer, do these five things to boost your finances
Five things single parents absolutely have to pin down
The positive aspects of the proposal are that paid leave and its importance are now topics of discussion. "Policy policymakers are at least thinking creatively about how to do this," Johnson said. "But this might not be the solution. There are lot of red flags."
A statement on Sen. Rubio's website says the Urban Institute study fails to factor in the proposal's transferability, which the senator says is a key feature.
"The benefit will also be transferable between parents in the household," Sen. Rubio and Rep. Ann Wagner (R-MO), wrote last month. Stay-at-home moms and dads, as well as working parents, would be eligible to take this option.
Sommerhauser says she finds it distressing that the legislators and Congressional representatives drafting these proposals are mostly middle-aged or older men who won't have to worry about a pension.
"They will never have to worry about hospital bills or if their parents get sick," Sommerhauser said. "To them, $13,000 is nothing to pay back. [But] that is a lot of money for people that are not in their income group."
Gambling that you will be able to delay collecting Social Security benefits is a decision few can make with certainty. "When you're 35, you have all these ideas about what you're going to do when you retire," Sommerhauser said. "You have no idea how the winds are going to buffet you in life."