The goal of distributing the vaccine inside the West Wing is to prevent additional government officials from falling ill in the final weeks of the Trump administration. The hope is to eventually distribute the vaccine to everyone who works in the White House, but will begin with some of the most senior people who work around the president, one of the people said.

It is not clear how many doses are being allocated to the White House or how many are needed, since many staff members have already tested positive for the virus and recovered. While many Trump officials said they were eager to receive the vaccine and would take it if it were offered, others said they were concerned it would send the wrong message by making it appear as if Trump staff members were hopping the line to protect a president who has already recovered from the virus and bragged that he is now “immune.”

The first doses of the Pfizer-BioNTech vaccine left a facility in Michigan early Sunday, with UPS and FedEx teaming up to ship them to all 50 states for distribution. A White House spokesman did not respond to a request for comment.