In his Thursday memo, Mr. Pichai noted that Verily is “part of our Alphabet family” and could assist in the coming “days and weeks” to respond quickly. He attached a link to a form where Google employees could volunteer to help. Over the next day, more than 1,700 signed up, a number that was communicated to Mr. Kushner’s team.
On Friday, reeling from the collapse of the stock markets and warnings by health experts of the virus’s rapid spread, Mr. Trump scheduled an afternoon news conference.
In the hours before the president’s appearance, Mr. Kushner’s team prepared a poster showing how the website might work; it did not mention Google specifically, but a flow chart showed that a “screening website” could provide “new options for consumers” around the country as they seek to find out whether they are infected.
During the news conference, Mr. Trump was enthusiastic.
“I want to thank Google — Google is helping to develop a website,” he said. “It’s going to be very quickly done, unlike websites of the past, to determine whether a test is warranted and to facilitate testing at a nearby convenient location.”
Moments later, at Mr. Trump’s invitation, Dr. Deborah L. Birx, who is coordinating the response to the virus, held up Mr. Kushner’s poster, saying that it represented a “new approach to testing, which will start in the screening website up here, facilitated by Google.”
The initial reaction 3,000 miles away in Silicon Valley was swift.
Mr. Trump’s comments caught Google completely off guard and executives rushed to issue a statement on Friday afternoon to temper expectations, making it clear that the website is an effort led by Verily, not Google itself. Carolyn Wang, Verily’s spokeswoman, said the plan was to start a pilot website for testing locations in the Bay Area but offered no timetable for a broader rollout.
On Friday evening, Mr. Kushner and Mr. Pichai spoke about the website for the first time, according to an administration official.