State Rep. Timothy Horrigan made the remarks Wednesday night in a thread discussing the Alaska plane crash that killed former Sen. Ted Stevens.
"Well a dead Palin wd be even more dangerous than a live one...she is all about her myth & if she was dead she cldn't commit any more gaffes," Horrigan wrote.
Horrigan was commenting on another post by a Democrat running for the state house, party activist Keith David Halloran, who found himself in hot water Wednesday after writing about the crash: "Just wish Sarah and Levy [sic] were on board."
After the controversy quickly gained steam Thursday, Horrigan sent a letter to the Speaker of the New Hampshire House offering his resignation.
"I apologize for thoughtless remarks I made which have brought this House into disrepute," Horrigan wrote. "I enjoyed my time in the House and I thank you personally for your support over the years."
Ryan Williams, a spokesman for the New Hampshire Republican Party, said Democrats in his state have "a widespread fixation" with Palin's death.
"Instead of discussing their failed economic policies, New Hampshire Democrats are now spending their time openly discussing Governor Sarah Palin's death," Williams said in a statement. "Rep. Horrigan's comments are sick, twisted and disgusting, and they must be immediately denounced by Governor John Lynch and Rep. Carol Shea-Porter.