45-year-old Debra Burt typed "Cameron - I'd like to egg him" on a friend's timeline.
British detectives spent a month tracking down her and ordered her to stay away from Cameron.
Debra said she made the quip out of frustration against cuts imposed by the government.
She accused cops of "snooping" on Facebook and told them: "Go out and fight real crooks."
"I'm not a terrorist. I'm just a middle-aged woman who made a jokey remark. I'd like to chuck an egg at him but I'd never do it. I'm just unhappy I can't find more work," she was quoted as saying by the Sun.
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Debra made the remark during a chat about Cameron's trip to Kent last week to see the Archbishop of Canterbury sworn in.
Two detectives knocked on her door in Ramsgate the day before the ceremony and said they had been hunting her for four weeks.
They had scoured her Facebook site, tried an old mobile number and called at her former address.
A Kent Police spokesman said officers did monitor Facebook ahead of Cameron's visit.
"We responded to information that someone was going to throw an egg. Officers visited the person and were satisfied there was no threat," he said.