WASHINGTON — No gainfully employed person can predict what their workload will look like the moment their children arrive, or how taxing it will be to put those responsibilities aside and care for a newborn 24/7 — let alone two of them. For Pete Buttigieg, the transportation secretary, that moment came just as political stakes for his boss were rising.

After a year spent trying to adopt, Mr. Buttigieg and his husband, Chasten, welcomed twins named Penelope Rose and Joseph August in August. The babies arrived amid the delay of a bipartisan infrastructure bill and growing concerns over product shortages and the sluggish transport of goods, inconveniences that have only grown more biting as the pandemic continues.

On Friday, Mr. Buttigieg’s twins cooed in the background as he spoke by phone about the “pro-family” policies in the Biden White House that enabled him to take paid time off. But then he shared a truism that countless people who have had children learned the hard way, and one that very few men in power have talked about.

“The big thing is having a newly personal appreciation for the fact that this is work,” Mr. Buttigieg said. “It may be time away from a professional role, but it’s very much time on.”

Taking time with his family meant that Mr. Buttigieg, who is admired inside the administration for his deftness as a public speaker and on-camera surrogate, was not front-and-center as infrastructure and supply chain discussions unfolded. He took four weeks of paid leave from his role where he was mostly offline, but said he was able to delegate responsibilities during leave or log on remotely for higher-priority work.

Mr. Buttigieg said that everyone in the White House, which sanctioned his leave as a cabinet member, had been “wonderfully supportive.” (As a senator, President Biden made it clear to staff in a memo that they were allowed to put family obligations before work.) But, Mr. Buttigieg added, taking paid leave “shouldn’t be up to your particular good fortune” or the graces of an employer.

Mr. Buttigieg said he was now better positioned to plead the case for better leave policies, though he expected he would be more focused on the particulars of the infrastructure bill than the parental leave provisions.

Still, conservatives questioned Mr. Buttigieg’s decision to take time off as legislation hangs in the balance and amid a supply-chain crisis. Loudest among them, as usual, was Tucker Carlson of Fox News: “Paternity leave, they call it, trying to figure out how to breastfeed. No word on how that went.” (Mr. Buttigieg said later that Mr. Carlson might not understand the concept of bottle feeding.)

Mr. Carlson’s comments were criticized as sexist and — since Mr. Buttigieg is the first gay cabinet member confirmed by the Senate — homophobic. Senator Tom Cotton, Republican of Arkansas, criticized Mr. Buttigieg’s performance as “so bad that Americans didn’t even realize he spent the last two months absent on paternity leave,” an insult that exaggerated how long the secretary was out of the office.

Senator Tammy Duckworth of Illinois, a Democrat and the first senator in history to give birth while in office, said those comments only highlighted the gender discrimination that fathers continued to face when they take parental leave.

“It is important for him to set the standard for other folks and make it acceptable,” Ms. Duckworth said in an interview. “It’s just as important for fathers to be there as mothers to be there.”

Research shows that parental leave helps fathers bond with their children, and a growing number of companies have extended benefits to fathers, but there is still evidence that men — both in the United States and elsewhere — feel more pressure to remain on the job rather than take time off to spend time with their babies.

The White House has stood behind Mr. Buttigieg’s decision. Jen Psaki, the White House press secretary, said on Twitter on Friday that he was a role model when it came to demonstrating “the importance of paid leave for new parents.”

At different points throughout their time in Washington, the Buttigieges have used their influence as public figures to advance cultural discussions and subvert commonly held ideas about the relationship dynamics of powerful people.

“People are accustomed to politics looking a different way, and you’re here to make sure that, you know, it can look a different way,” Chasten Buttigieg said in an interview with The Times in the spring.

The next frontier for the Buttigieges is parenthood, and Mr. Buttigieg says they are learning on the (unpaid) job what research has made clear: Time allowed for parents to bond with their children after birth is crucial for development.

And yet, Americans receive no mandated paid federal leave. (The 1993 Family and Medical Leave Act provides for up to 12 weeks of unpaid time off.)

When both parents are able to take leave, it eases a burden that has historically fallen on parents who remain at home. Some nine states and the District of Columbia, where the Buttigieges live, have or plan to institute some version of paid family leave. Federal workers can receive up to 12 weeks paid leave.

That time has been shorter or nonexistent for cabinet members, who are not subject to federal leave provisions. A spokesman for Julián Castro, a former secretary of Housing and Urban Development, told Politico that Mr. Castro took a “week or so” of leave after his child was born.

Mr. Buttigieg’s decision to take time off came at another pivotal moment for the administration: Mr. Biden is trying to get his party to agree on the particulars of a sprawling bill that would include 12 weeks of paid parental leave. It is unclear whether the provision will survive negotiations with the party’s centrists, who have demanded a smaller price tag in order for the plan to pass. But supporters of the parental leave provision argue it is a necessity for America to remain competitive.

“If we remain one of the only countries in the world without paid leave during an ongoing pandemic, that will be an added tragedy and a failure of our government,” Dawn Huckelbridge, the director of Paid Leave for All, said in an interview. “What I hope comes out of this is a reminder that every single one of us is going to have to give and receive care in our lifetimes.”

This week, Mr. Buttigieg began ramping up at work again by joining meetings with the president and appearing for media interviews, though a spokesman said he would take more time off in the future to be with his family.

On Friday, Mr. Buttigieg spoke about his time on leave as he prepared to appear on Fox News and, later, MSNBC. His time off allowed him to see that his children, now two months old, have different personalities, and that they prefer sleeping on their fathers’ chests to any baby swing or bassinet.

“It’s one thing to believe something as a matter of policy,” Mr. Buttigieg said about his time off bonding with his twins. “It’s another to live it and see how much of a difference it could make.”