Miller's spokeswoman said an orchestrated group posing as a grassroots organization was demanding town hall meetings so they could disrupt them.
She said the caller wanted a town hall meeting and told a staffer "it could cost him his life."
The staffer asked him to repeat the comment and he did.
The staffer then reported it to Capitol Hill Police, who are investigating.
Congressman Miller has said he largely supports President Obama's proposals for health care overhaul.