With Father’s Day approaching, dads are starting to get some much-needed attention. The Obama administration on Monday convened the first-ever White House event focused on working dads and the impact of corporate policies like paternity leave and workplace flexibility.

Just a few decades ago, new fathers were often barred from the delivery room when their wives gave birth. But dads today expect to be fully present, not just for the big moment but also for the days, months, and years to follow. This subjects them to the same work-family conflicts that working mothers have experienced for decades: juggling responsibilities at home and at work simultaneously.

Only 12% of U.S. employers surveyed by the Society for Human Resource Management offer paid paternity leave, a stark contrast to the 70 other countries that have legislated paid paternity leave. Some dads can cobble together sick leave and vacation time to be present for the days after a new child joins the family. Those who take time off from work rave about the opportunity.

“It was a fabulous experience and I couldn’t imagine not taking it,” says Marc Carlson, 35, a Detroit-based senior manager at Ernst & Young, who took six weeks of paid leave after the birth of his baby Rebecca last year. “It was a great time for me to bond with my new daughter and feel that I was playing a critical role in my family transition.”

Rebecca ended up having food allergies and colic, making his hands-on parenting all the more important. Carlson took two weeks off immediately after the baby arrived to be home with his wife and the remaining four weeks after his wife’s maternity leave ended. “When I was there on my own was the highlight of my year,” he says, praising his colleagues, supervisor, and employer for not interrupting his time at home with calls or emails.

Some dads encounter negative repercussions for taking paternity leave. Famously, New York Mets second baseman Daniel Murphy became the subject of critical headlines and radio talk show vitriol after he skipped the first two games of the season to be with his wife in Florida for the birth of their first child. “When Noah asks me one day what was it like when I was born,” Murphy said at the White House event, “it’s going to go so much farther that I’m the one who cut his umbilical cord. Long after they tell me I’m not good enough to play baseball anymore, I’ll be a father and I’ll be a husband. I wanted to be there for my wife and my son.”

Research by Jennifer L. Berdahl, an associate professor at the University of Toronto, found that men who cared for their children more than the norm experienced workplace mistreatment. At the White House event, University of Oregon sociologist Scott Coltrane said a longitudinal study of 12,000 individuals found men suffered lower lifetime wages to a similar degree as women when they took time away from work to care for children, whether as leave or as a part-time schedule.

Two weeks seems to be a safe length of paternity leave before men grow concerned they might face blowback, according to Brad Harrington, executive director of the Boston College Center for Work and Family. That’s the average length of paternity leave used, favored by 39% of dads, according to a new report from the center, which surveyed 1,029 fathers from 286 different employers. A majority of the responses came from nine companies that are members of the center, meaning the data pool may reflect a more progressive and family-friendly set of companies than the norm. Indeed, 67% of the dads surveyed had access to paid paternity leave, less than the 75% in the Working Mother “Best Companies” list but greater than the national average reported by SHRM.

“There is still in many people’s minds the expectation that taking more than a week or more than two weeks might not be appropriate. They might not be seen as committed to the workplace,” Harrington said during a conference call with journalists last week. He discussed his research at the White House on Monday, after remarks from Chief of Staff Denis McDonough, Labor Secretary Thomas Perez, and chairman of the Council of Economic Advisers Jason Furman.

A whopping 99% of men Harrington surveyed felt that companies should offer paid leave to new dads, says Karyn Twaronite, a partner at Ernst & Young, which sponsored the research. Nearly all Ernst & Young employees eligible for paid leave have taken it, and the firm considers it important for retention, productivity, and engagement.

The survey found that 89% of men would consider paid paternity leave important if they were looking to move to a new employer and considering having a child. But even a majority (88%) of those who received no paid leave took time off, the report found. Three-quarters of fathers would prefer the flexibility to take the time off as needed, rather than immediately after the child’s birth, Harrington says.

Jonathan Keane, 36, took five days of paid leave from his job as director of customer service at communications technology firm Bandwidth, when his son Henry was born earlier this year. “It made a huge difference at home,” says Keane, who’s based in Raleigh, N.C.

Thinking back to when his two-year old Carter was born, when he worked at a different company, he recalls not feeling fully present despite it being one of the happiest days of his life. “Some of me was still feeling the pressure from having to check in at work,” he says.

Richard Ellenson, a Concord, Calif.-based technical editor for a government contractor, plans to take five weeks off when his wife gives birth, any day now. Because he’s been at the company less than a year, he doesn’t qualify for employer-paid leave, but California’s family leave program will cover 50% of his pay. At the White House event, Furman noted that more than 90% of California employers surveyed reported no problems implementing the leave program.

“I am very comfortable taking off this time thanks to my supervisor’s full support,” he says. “You have your whole life to work, but you don’t have your child’s first waking moments forever.”