Less than two percent.
Of the hundred billion dollars and change that Americans spend each year on child care and preschool, less than two percent of that comes from private-sector employers. A bit under a third comes from the government, via both directly-run facilities and subsidized private-sector ones. The lion's share comes straight out of parents' thinly-stretched wallets.
It's not that employers are generally stingy. The clear counterexample is health care: employers pay around 20% of all US healthcare costs, and close to half of the costs of care for working-age adults.
The difference here is basically due to a historical contingency. Generous health care offerings were a way for employers to attract workers in the 1940s, when regulations and high marginal tax rates discouraged competing directly on wages. That led to further legal changes favoring employer care (in particular, favorable tax treatment), which led to more entrenchment of the model, and ultimately to health care becoming a non-negotiable for employers hiring middle-class people.
So employer health care is now part of American culture. But that culture emerged downstream of laws and regulations. By contrast, for decades the law did nothing to encourage employer-provided child care, and often outright discouraged it. That's started to change, but few employers and fewer employees are aware of these changes.
And this is where my company comes in. I'm building ways for employers and employees to understand the changing environment and how to benefit from it, while surmounting the still-significant obstacles to creating employer-supported care.