Edwin Donovan, a spokesman for the Secret Service, said the agency will take "appropriate investigative steps" in connection to the survey, which was posted on Saturday and was quickly removed when Facebook employees were alerted to its existence.
"We are continuing our investigation," Donovan told FOXNews.com, declining further comment.
The poll asked respondents: "Should Obama be killed?"
The possible answers were "no," "maybe," yes," and "yes if he cuts my health care."
Facebook spokesman Barry Schnitt said a "third-party application" enabled an individual user to create what he said was an "offensive poll."
"The application was immediately suspended while the inappropriate content could be removed by the developer and until such time as the developer institutes better procedures to monitor their user-generated content," Schnitt said in a statement to FOXNews.com.
Facebook is now cooperating with the Secret Service, Schnitt said.
"This is the kind of garbage that's generated from the extreme right against Obama, and it's going way over the line," Beckel told FOXNews.com. "It's got to be stopped. Find him, prosecute him and put him in jail."
Regardless of political persuasion, Beckel said such threats are "un-American" and simply not acceptable.
"If they don't like what Obama is doing, then maybe they ought to go out and vote for someone else," he said. "But relying on this kind of attack is un-American and unacceptable."
In November, prior to Obama's landslide election victory, officials from the Secret Service declined to comment on the number of threats he had received, but they said they saw more threats against him than any other candidate during the campaign.