This claim is false. Mothers and fathers put in equal work. The definitive source for what Americans do is the American Time Use Survey, which gathers representative data on tens of thousands of households. Total work hours are the combination of paid work, unpaid work (such as household work) and childcare. Here is a section of All In summarizing what the ATUS shows:
Today’s dads and moms work equally hard on behalf of their families. When you combine paid work with household chores and child care, they put in just about the same amount of time. And we’re talking a lot of hours. On average, dads put in about fifty-four hours of work time to moms’ fifty-three. In two-income homes, moms work fifty-nine hours to dads’ fifty-eight. In single-income homes, the breadwinner works more overall. And although the number of female breadwinners is on the rise, dads are still the vast majority of primary or sole breadwinners.
You can see this section of All In for free here. It includes a citation to Pew Research, an organization that gets plenty of things wrong, but got this right.
Anytime you see a “researcher” claim that moms do more work, look at the the methodology. Often it’s a tiny, non-representative sample — and therefore meaningless.