The Governor's office and the Guam Memorial Hospital have stepped up security after death threats aimed at the governor and the hospital administrator.
The threats and recent cases of vandalism are linked to the hospital's privatisation plans.
The hospital's administrator says the proposals involve the outsourcing of services like maintenance and security.
Mr McMillan says vandals have damaged cars and equipment, including machinery which cared for premature babies.
He says police are taking the matter seriously.
"I would hope that these are just angry people ventilating but the potential for violence is real and present. Guam like the United States has a pretty liberal gun control. So that anybody that wants a gun can provide one. So we like to take these things seriously because we don't want to lose anybody."
Bill McMillan says the level of feeling is because government positions are well-sought after, because of the attractive benefit scheme.
The Governor's office wouldn't comment on security matters.